Can't get the starter out pass the cat on my 1987 corvette as shown in repair manual

The fuel pump relay in the 1991 corvette is located under the IP on the pass side.
Open pass door, unscrew two screws under the glovebox take off the fuse panel, unscrew third screw to plastic plate underneath glovebox, pull away carpet , pull down plastic plate under the glovebox you will find a number of fuses and relays if you reach in under there-their in a row, one in the middle is the fuel relay, and they are the same https://www.google.com/search?q=1991+corvette+fuel+pump+relay+location&rlz=1C1CHBF_enUS812US812&tbm=isch&source=iu&ictx=1&fir=22ZCtfxXLAJIhM%253A%252CT6ISkStpACZ3fM%252C_&vet=1&usg=AI4_-kQcWSXh1X3gyHRgNaeIT01QKiHSbQ&sa=X&ved=2ahUKEwi72ajMpdviAhUCZN8KHRgdBRQQ9QEwAHoECAUQBA#imgrc=22ZCtfxXLAJIhM: https://www.google.com/search?q=1991+corvette+fuel+pump+relay+location&rlz=1C1CHBF_enUS812US812&tbm=isch&source=iu&ictx=1&fir=22ZCtfxXLAJIhM%253A%252CT6ISkStpACZ3fM%252C_&vet=1&usg=AI4_-kQcWSXh1X3gyHRgNaeIT01QKiHSbQ&sa=X&ved=2ahUKEwi72ajMpdviAhUCZN8KHRgdBRQQ9QEwAHoECAUQBA#imgrc=zm66sLFTaleu2M:&vet=

It's telling you that the red wire is number 5 wire on the wiring diagram or the number 8 wire in the harness is white.

Any of the mechanical parts on a Corvette can go work. There aren't any specific problems associated with the cars.
if you need an ecu chip tuning tool you can click here: ecu chip tuning tools

There should be a starter fuse mate not to sure where might be in engine bay

Probably burnt out. Replace!

Underneath the car, for a front wheel drive, it will be toward the front of the engine a long cylinder shaped part with another cylinder with wires going onto it. take the wires off first, paying close attention to their placement, then you remove the mounting bolts and pull it out, it's that easy dude, you can also find a video on how to do it on youtube.

LIGHT SWITCH 15 AMP FUSE CIRCUIT BREAKER / TAIL , DOME , COURTESY 10 AMP FUSE / MANUAL RADIO 4 AMP FUSE / AUTOMATIC RADIO 7.5 AMP FUSE / HEATER 10 AMP FUSE / AIR-CONDITIONER 20 AMP FUSE / BACK UP AND BRAKE ON 10 AMP FUSE / POWER ANTENNA 15 AMP FUSE. THE ELECTRICAL BOOK DIDNT HAVE A DIAGRAM BUT IT TOLD WHAT AMP EACH COMPONENT USES AND VOLTS FROM GENERATOR. IF YOU HAVE A 55 CORVETTE YOU HAVE 6 VOLT ELECTRICAL SYSTEM.IF THIS DONT HELP YOU CAN GO ON LINE AND BUY A 59 CORVETTE REPAIR MANUAL.

replace blower control module

you can try bypassing it like this turn the key on then take a screwdriver and touch the 2 bolts on the starter try that or try changing the fender mounted starter selonoid

yes you will need both cats to pass depending on where you are. i have had 3 broncos and im drivng one now and cut one off and have the muffler and one cat and it passed. as long as your not in california i think you will be fine with just one