That sounds like a good plan! Is the incubator already built and that's why you can't get the other kind? I think it should work as long as you watch it closely :)
Here is a link :)
https://www.backyardchickens.com/a/homemade-easy-cooler-incubator
She also has a cabinet incubator somewhere too but you're probably not hatching that many eggs :P
But it's a really easy step by step guide and she has lots of other tips on incubating too
Yeah, i dont see the point in spending so much especially when a homemade one can hold way more haha
Planning is always good and I hope you get lucky! Haha