I'm not familiar with the particular "kit" that you mentioned. If it has fittings, and oil, then it won't hurt anything if you follow a lot of other procedures and have the right equipment to do the job.
If it is as many kits with a hose and a can of snake oil and some 134, these are called DEATH KITS! Not your death, but the death of the a/c.
R12 is coming down in price and is ALWAYS your best approach. If you INSIST on converting, you must RECOVER the existing refrigerant, put in Ester oil, thoroughly evacuate and then charge with 134. This is a MINIMUM approach.
To really do it right, you flush the entire system, pour out as much oil as you can from the compressor, replace the accumulator, replace the orifice tube with the correct one, put in Ester oil, thoroughly evacuate and charge.
When you go to 134, you lose about 15% of your a/c's capacity. Some cars won't tolerate this, they just don't have the reserve capacity. In your case, you don't live in a hot climate and the Vette a/c has plenty of capacity anyway.
I converted my '88 a few years back when R12 was still very expensive and it worked out well for me. I did not, however, use a death kit.
Best of luck,