Sure, what you say is entirely possible. But here's how I interpret what I saw and heard on screen:
Starfleet sent 40 starships to combat the Borg in BoBW. They were all destroyed. The dialogue from Shelby seems to indicate that these 40 ships represented the majority of ships in Starfleet, although DS9 would later show that Starfleet has thousands of ships.
That and the way registry numbers have expanded so drastically since the days of TOS and the Movies.
What dialogue are you referring to? I can recall nothing where she indicated that that was the bulk of the fleet.
She also said that the fleet would be rebuilt within a year, but most of the ships we saw in DS9 were Excelsiors and Mirandas, which were clearly not new. The vast majority of the other DS9 ships were the Akira, Saber and Steamrunner classes. If those classes weren't new either, then where are all the new ships that Shelby's talking about? So how do we justify all this?
Well first off, there's nothing to stop new batches of older designs being ordered (as we know happened with both Excelsior and Miranda classes at the very least, and IINM, the Nebula variants also).
Secondly, I'm going to employ the dreaded Real Life Production Reasons card, as we all know very well by now that DS9's VFX were hampered by both budget constraints and damaged/unuseable/unavailable CGI models (otherwise we'd surely have seen other classes, such as the oft-bemoaned missing
Ambassador)
I'll also include in this instance the unnecessary dumbing down by TIIC wherein stipulations were made not to use the Enterprise-E model on DS9 in case it caused "confusion". Dumbasses....
Third, it still doesn't prohibit mid age-range designs having been refit - designs that may have been classed as frigates and so on during the Cardassian war could have been since down-graded, and now revised upwards once again post-refit to fill noticeable gaps in fleet capabilities.
Fourth, there's nothing to say that designs such as the
Intrepid, Bradbury, Yeager (even though its onscreen representation was hideous) etc, weren't created to backfill roles left empty by the decimation of the fleet. Remember, even though almost 40 ships were destroyed, they were clearly never designed as "anti-Borg vessels" to begin with, so their loss would have left gaps in regular fleet capability that needed filling.
Here's my take: Most of the Galaxy-style ship designs were relatively new as of the start of TNG.
The Nebulas had IIRC been around for a good 5-10 years, while smaller classes (such as the New Orleans) had it seems been around since the 2340s. Likewise, I'd say based on registry and appearance that the Niagara, Springfield, Challenger, Cheyenne, and Freedom classes had been around for a bit also.
Those new ships were what Starfleet mostly used against the Borg at Wolf 359 because they represented the best that Starfleet could throw at this new powerful threat. Yes, there were lots of older ships like the Excelsior and Miranda classes, but either Starfleet didn't think they'd be much help, or they vastly underestimated the Borg threat by not using them (probably a bit of both).
Apart from some Nebulas, I see no evidence of this thus far. Was an official list ever provided, including vessel classes and reg numbers?
ETA: Apologies, I just did a quick check and it seems Adml Hanson's flagship was supposed to be a Galaxy, though it remains unnamed so far as I know. Having said that though, it is only one ship!
Also, as I recall during BoBW Pt1 Starfleet was surprised that the Borg had arrived so soon after the events of "Q Who", and dialogue mentioned that they were using everything they
had available (ie, in range); but not necessarily all of their best/most powerful assets - in fact I'd expect most of the newer Galaxy types to be off exploring and thus out of range, although the Nebulas I suspect were a significant presence.
I doubt SF underestimated the Borg threat, but that rather they simply didn't have the time to prepare and develop their defences they way they'd have liked (not that that would guarantee any better results!
)
The destruction of 40 top-of-the-line ships while leaving older and outdated ships still functioning could have been considered a huge loss for Starfleet, justifying Shelby's comment.
Again, I don't see evidence that the fleet was primarily top-of-the-line, either from the hulks shown in the aftermath, or during the scenes shown in "Emissary". And Shelby's glib attitude about having the fleet "up and running within a year" suggests it isn't a huge task to replace such a relatively small number of vessels.
By the time of the Dominion War Starfleet realized that they'd need all their ships, not just the top-of-the-line ones, which is why we saw old designs along with newer ones, and considerably more than 40.
I sort-of-agree with this. I imagine a lot of previously decommissioned/mothballed vessels were recalled into service after undergoing bare minimal refits - either post-Wolf 359 to fill aforementioned gaps in the fleet, or as you suggest, due to Starfleet rapidly moving to prepare for war with the Dominion. The use of those vessels may of -at first- been simply intended to bolster the fleet so as to allow newer vessels to be taken off their assigned duties temporarily and, oh, I dunno... maybe refit to a more modern spec!
...new ship classes such as the Akira, Steamrunner, Saber, Defiant and Sovereign, specifically designed to combat the Borg, which was why they were used in the Sector 001 battle in FC. YMMV.
YMMV indeed, as I don't accept the Akira as a new design! Rather it looks to me like something that debuted with a registry in the 55000s range, and has since been upgraded to a minor extent (lifeboats being the most noticeable change)...
But then, if I could do that I'd draw up a pre-refit Steamrunner, et.al. 
I say we rationalise it as this having been the bulk of the "home fleet" and thus most seen and recognised by the core worlds -- with the vast majority of vessels assigned further out...
