Not that much. Assuming that the cockpit really is the size of the Type 15 shuttlepod from TNG (as per the interior, which was shot using that prop), and assuming that the outer wing panels fold at the obvious lines, these things could be shot out of fairly small doors folded up and then deploy those wingtips (which preclude landing on a level surface anyway)...
The Steamrunner certainly has much bigger doors, basically Galaxy primary shuttlebay size, but even her putative "bow doors" (those fancy blue things in the bow cutout) would seem sufficient for spitting out folded-up attack craft.
...Which is another thing we ought to consider: those craft were officially "attack" units, which is classically terminology for (air)craft that don't fight other (air)craft, but instead strike at ground targets - or, just possibly, ships. It's quite possible that these fighters have no real anti-ship role or capabilities, which is why Sisko was so solemn about sending them to their deaths against Cardassian ships in the battle to retake DS9. OTOH, we've seen Steamrunners fare rather poorly in ship-to-ship: in DS9, they practically never manage to fire any weapons, and there and in ST:FC, they appear to be the ships Voted Most Likely And Numerous to Go Down in Flames in No Time Flat. Perhaps that's a match made in heaven, and Steamrunners chiefly exist to deliver those attack craft to planets in need of some attacking, much like today's LSD or LST ships (or at most LPH or LHD/LHA ships) rather than aircraft carriers...
The Akira is a different beast, frequently seen firing weapons and sometimes even scoring some results (even though funnily enough, only the Defiant and the Galaxy class ever score any actual onscreen kills in the Dominion War). Not sure if she'd really be a fightercarrier or a LHA, or even a cruiser-carrier like the old Soviet Kiev, despite having a shuttlebay or two. But I wouldn't blame Starfleet for having a "hybrid" ship type or two for frontier use, for bush wars of all sorts that could use a little bit of cruiser, a little bit of carrier, a little bit of planetary assault ship.
Timo Saloniemi