It can be done, and you have started going about it the right way.
The complete subframe can be dropped on the donor car and transplanted into the 93. All wiring should be used. You will also need to replace the dash wiring, as well as fuel pump and gauge cluster I believe due to differences in the fuel level voltages. Since it is a 93, you'll probably also want to swap over the ECC unit and controller to have the selectable climate control. You'll need to keep your dash since 93 had the hand release for the e-brake and the 97 had the foot pump one, unless you want to swap that over.
Basically, the body'* are exactly the same (shell wise) and you are just going to be transplanting the internals.
Good luck with it. Let us know how it goes. The Factory service manuals for both cars will be invaluable for this project to be able to look up differences.
2007 Saturn Aura XR | 1970 Chevy Blazer 4x4 | 1970 GMC 3/4 Suburban 4x4