Actually there are special tools that are sometimes needed yet most of us will not find out about untill such time as they are needed.
If the OP is still present then take a good hard look at what you have and if storage is really a problem then ask yourself which tools do you use frequently and which only once every few years.
My boat is similar in size to yours at 32' also. I carry a set of 1/4, 3/8 and some 1/2 drives along with deep sockets and extra extensions for each.
The usual combination wrenches, a butane soldering iron, crimpers and cutters for electrical repairs, Vise grips, pliers of several different types, adjustable wrenches, filter wrenches for my filters, hacksaw & blades, a folding drywall saw with blades for cutting rope wound around the prop, large selection of screwdrivers, small 18" prybar, DMM, clamp DC ammeter, battery oper. drill both 18V & my old 7V , 150W inverter to recharge the drills, Full set of inch drill bits to 1/2", various files, Allen key sets, small selection of metric sockets and wrenches to suit the lack of metric stuff aboard, 2 pipe wrenches, 2 packing nut wrenches, .
I know I have forgotten a lot of stuff but it all goes with me. THere are some things that get left at home normally but on the long trips I take extra stuff in addition.