You can do what was suggested above. Or you can just go to Walmart and buy the conversion kit. Then go to harbor freight and buy the air operated vacuum pump and the r134a gauge set.
Put the conversion fittings on, and then take the vacuum pump and gauges and pull a vacuum on the system. See how long it holds vacuum to see if you have any major leaks.
If it holds vacuum, get a jumper to jump the low pressure switch, get the compressor running, and then dump the conversion cans into the system. They have a ester oil mixed in the cans which is compatible with the old r12 oil in the system. No need to get all the old r12 oil out unless you want to go to that trouble.
The old r12 hoses after being exposed to the r12 and the r12 oil, become "pickled" and won't leak the r134a. Same with the old o-rings, unless you have a damaged and leaking o-ring.
So you won't get away without spending some money, but it will be a lot cheaper than paying someone else, and you will have some useful tools added to your shop.
harbor freight vacuum pump.
https://www.harborfreight.com/air-vacuum-pump-with-r134a-and-r12-connectors-96677.html $17.99
harbor freight gauge set.
https://www.harborfreight.com/ac-r134a-manifold-gauge-set-60806.html?_br_psugg_q=r134a $62.99