Whats the coil # on the original?

Not sure I'd use that one. It will work but I think the Williams coils will be significantly stronger than the bally having so few windings compared to the original.

You want to match the resistance specs of a coil and the bally is about twice the Williams'. They don't need to be exact, but the closer the better.
Your Bally is about 10 and the Williams is about 4.5.

https://flippers.com/coil-resistance.html can help you figure out what's close

I'm not going to lie to you, when a pinball is at a bar, and they've called you out on a Saturday night at 11:00 PM because they've still got four hours until closing...

I've put 23-800's in a pinball where I pulled a 26-1200.

This is known generally as a 'bad thing'.

It'll work, but it's too strong. You'll have premature failure of the pop bumper ring and in particular the steel link that connects the plunger of the coil to the pop bumper ring will be broken, possibly as early as next week. (Yeah, you know how I know this...)

For home use, I'd recommend putting the correct coil value into your pin. Good decision.

If I can get away with it, while I wait for the correct coil, I always put in one with higher resistance that's as close as possible. Sometimes it's fine other times it's just too weak. And of course if it's physically fried due to a closed switch or shorted transistor that has to be addressed first. If it's fried due to a broken coil winding wire that sometimes can be repaired if there is enough of it hanging out of the bobbin.