Fairly short stick. I would route the top side of my CP for that one. Assuming it is like a T-stick, you'll have to make a hole in the CP big enough for the body of the stick to fit in, and recess the mounting plate into the wood flush. I had to disassemble a T-stick to get the shape and the hole locations for the mounting plate, for the recess. Cut the recess first, the make the hole for the guts of the stick. You can use machine screws thru the mounting plate with nuts/washers underneath or wood screws if you don't just hammer on your sticks during play. I'm pretty rough on my sticks and they are just mounted using wood screws, but that is into 13 ply plywood, not MDF.
Of course this advice assumes that the j-stick and t-stick are very similar, and that you are covering the CP with art/plexi.