Best tools for woodwork project
This can probably be done with 4.5" hole saw which is pretty close to your dimensions.

I assume what you want is the disk, not the hole.

A circular disk can also be cut with a scroll saw.

Another tool is an adjustable circle cutter or fly cutter of which there are few different types. 

A circle can also be cut using a mill (or lathe) with a milling cutter in combination with a rotary table (or divider).