Why do you want to do this? Are you aware that in todays market R12 can be purchased for very little more than 134? Going to 134 will reduce your a/c performance by about 15% to 20%.
Although my 88 is converted, I did it many years ago. Since that time I have learned that it's a bad approach, most especially on a Vette. The system just doesn't have enough reserve capacity to tolerate it in most cases.
You can go online and get an EPA 609 license for $20 and an hour or so taking an open book test. After that you can buy all the R12 you want LEGALLY. R12 is available on ebay for about $10 a pound and from other sources for similar pricing.
With 134 prices where they are, you can't even buy the fittings and the oil for the difference in refrigerant cost.
I converted to R134A in my 84 back in 2000. It blows 46 degrees at the vent in 105 degree ambient temps. Here's what I did.
Replaced the compressor and clutch assembly
All new O Rings
New Orifice tube.
New Accumulator / Drier.
Flushed all lines, evaporator, and condensor. Pulled a vacuum on the system for 3 hours. Recharged with PAG oil and 45 psi on the low side with R134A. In 9 years, I've had to add 2 cans of refrigerant (the first in 2004, the second about a month ago). I've been very happy with the conversion, and I live in a very hot climate.
So it's up to you. There's really no right or wrong answer whether to convert or not. R-12 will blow colder, but how cold is cold enough for you?
I’ve been lucky and just as Frizlefrak stated it will cool. We did one of my cars this way and did not change parts. We replaced the O-rings and flushed the system. Our compressor was fine the system was leaking at one of the connections. Now remember this was when R12 was on a scale with gold. It seems like it takes a long time to get cool but once it gets cool it is fine.
You can go one step further and my lesson was learned on older C2-C3 conversions.
The 134 systems on the newer cars do not use the old fin and tube condenser like the R12 systems. The fin and tube style will work, but not as well with 134. Without changing the condenser it will hinder the ability of the system. 134 cars used a different style condenser made just for 134 systems. Changing the condenser to one designed for the 134A Freon will give you a much better end result.