Hi and welcome!
IKEA doesn't do ANY custom work...they simply contract out with various local fabricators. If you purchase one of the IKEA stock countertops, you're on your own in terms of modifying them.
I would suggest you check the specs for your cooktop to find out what the manufacturer has to say about flush-mounting and all the other specifications you'll need to meet for a safe install. Once you know that it is allowable, then you can decide if you'll have a fabricator prepare your countertop or if you can
DIY
or hire a handyman to modify your wood countertop.