You won't be cutting up a full cap.
You'd be cutting up a 'topper', which is a smaller piece to begin with.
Cutting up a full cap just means you're buying more (larger) therefore paying more and ultimately throwing away more.

Its a complete waste if you're only interested in using the front part anyway.

You have to decide if you are buying a ready made topper (stock) and hoping it matches your own hair in colour & density & hairline contour. Or, are you going to have a piece made (custom) to your specifications?

If you're having a custom piece made, then you have it made to the exact size you need, so you don't have to do any lace cutting.
If you're buying a stock piece, you can cut the lace yourself and its not that difficult using a craft blade.

So you have to decide which way you're proceeding before you can be advised any further.