Gouf,
Excellent, excellent work, especially on the York. A have a couple of personal nitpicks/concerns. In the "Expanded" Trek Universe, the York is supposed to have been a name of a ship that Christopher Pike commanded before the Enterprise, and before Yorktown, if I remember things right. I just wondered if you intended it to be the same ship?
A "cutter" is normally an oversize boat, equivalent to a modern Cost Guard Cutter or a Naval Patrol Boat/Craft (PT). I- would typically have a crew of 10-20, and be about 30 feet long. Treknologically/expanded universe speaking, normally Federation cutters don't use a saucer primary hull, they tend to be rectangular, a bit like an oversized DS9 runabout. What I think you've designed is best classifieds as a Light Corvette or a Light Frigate. Larger Corvettes would have two engines and an extended or small secondary hull. Light Frigates would normally have two engines, but would look pretty similar to what you have.
Without having dimensions to work with, its hard to be precise, but using my eyeballs I would think that a crew of 40 might be a bit more reasonable, considering its still got all the characteristics of a larger starship and would therefore need about as much maintainance.
As to the registry number, this gets tricky. The problem is that we have two many designs (at least with too many constructed ships) from too many sources to cram them all in. This number would work with with the Starfleet Battles system, but in "Canon" terms would date to early in the UFP. I don't really have a good suggestion at the moment as to an alternative, but thought I would mention my consternation at the registry system issue in passing.
Please don't take these comments the wrong way, they are thoughts and suggestions, and not meant to detract from appreciation of your great skill.