You're going to get two sets of answers on that. One group of us is going to say the frames are different in regards to strength, one will say they are the same. Someone is going to say how their frame was fine, someone is going to say theirs broke under the weight of the Cummins. If the Club Cab is on a 3/4 or 1 ton truck, it SHOULD be pretty close and definately should handle the weight difference. I would get out there with a measuring tape, start checking widths, lengths, etc... If you are going just swap body parts, I would suggest a lot of study and measuring. Plenty of these projects have been done, but it does take time. Most likely, your wiring is "funky" on the 93, you might as well rewire or build a new harness. 93 also does have SOME stuff running off the primitive computer under the inner fender on the driver side, esp. if you go with cruise and a slush box. You will have to cut and paste to get the Intercooler to work on the 76 grill, so you'll need to massage some stuff with the radiator support/core area. You have all the parts, but the depth of work required to even do it half-assed means you might as well go all in and do it right the first time. Check out the First-Gen pics in the stickies - couple of really nice frame-offs that should give you some great ideas on scope of work and time frame. But they sure do turn out nice!
WARNING! I have not done a frame off with a First Gen! I did enough of that with Jeeps, so the idea behind "studying the frame" comes from the two different eras of emission controls, engines, transmissions, crossmembers, clutch and pedal systems, brake systems, etc. Go online to RockAuto and look at the different parts numbers for the different years, that may also give you some ideas. AND ... document what you did. Wiring, brakes, other wear components will be a pain in the butt to remember if you don't note this stuff. If you do make your own harness, write out or label what goes where. The next guy that owns your truck will probably pay an extra grand just to know what wire goes where and what year brake components are in it.
Good luck and keep us posted!