I would have some concern about the PSU in a 10 year old PC......regardless of the graphics card or what games I wanted to play.
On the other hand, the entire PC has little value, so it's difficult to recommend that you spend more money on it....rather than starting over.
A new decent power supply is probably going to cost 60 dollars on up.
If it did "blow up", how big of a disaster would that be and what would you do? Would you lose your job?
If the PC is purely for entertainment, you might want to just go ahead with your plans, realizing it could drop dead at any time regardless of what you do.