That's one way. Another is to organize everything as a kind of public offering.I can see the wealthy observers bribing the Romans to whip or burn the crucified
Auction off every step of the process.
If you can offer only a little bit of money, maybe you can fling the whip a few times at the victim.
If you have a bit more, maybe you can hammer in a nail or two.
If you can afford it and feel like spending, you can run the whole execution as you wish.
At the same time you are supporting the budget! All such contributions can be deducted from taxes.
I think that is how they often do it in the Garden of Unearthly Despairs that lies at the heart of the Despotate of Deliria.
There's just one thing to warn of. Every now and then a rich mindless fool falls in love with a condemned, outbids everyone and pays the sum for 'running the procedure at their whim', they think it's a grand idea for that whim to be taking the delinquent as their love-slave. The problem is that any transgression of that slave may have the Despot now seize the owner for crucifixion also. After all they took responsibility!