Yes, that's the goal. It's very easy. With as much room as you have there, I might even make two cuts just to make it easier. Even if you put a groove in that stud, the stud wont be ruined. You can definitely do the job without putting a mark in that stud, but even if you did....no big deal as long as it's not too deep.
Give it a go...you'll be glad you did. Plus, there are a million and one uses for a Dremmel tool. You should have one anyway.