Hi Linus, welcome to IKEAfans!
Since the sink is 10"D, I think a pair of 18"H x 15"W doors would work fine. You can then add a little filler (deco trim?) under the sink above the doors to fill out the remainder like Dulci said.
The larger problem will be the fact that your sink is 30" wide and the cabinet is 30"W less the 3/4" sides, only 28.5" interior width. I'll let Dulci or another with experience modifying help with that.
Can't wait to see progress pictures! What doorstyle are you using?
Best wishes,
Gloria