Cutting stud in load bearing wall to create vent opening for cooktop hood
The correct way is to frame the opening with a header, jack studs(aka trimmers) and king studs in the same manner that window and door openings are framed. See image below for reference. 

The header is typically made of two pieces of 2x lumber face nailed together, sometimes with a piece of 1/2” plywood between the two to make the depth of the header match the depth of the studs. You can probably use 2x6’s for such a short span. 

You can locate the trimmers and king studs to hang the vent hood on, while the cripples below the sill of the opening should be located 16” on center (or whatever the existing stud spacing currently is) in relation to all other studs in the wall. 

Of course, all of that wiring makes doing it the correct way difficult... What you are suggesting will work, but it is technically incorrect.