what do you mean blocking on the cabinet? To nail into it?
Well, liquid nail to. I don't like to put nails through the front if I can help it. It's just a couple pieces of wood about 2" wide with a 3/8" lip on the ends to fasten to the faceplate from the back side. Then the false front should just glue to it. If the sink wasn't in the way it could just be put on with screws.
I had a customer that had me make the sink false fronts removable and their kids kept pulling them off and dropping them of the floor. There is no telling how many times I had to go back and touch up the damage. Finally they got so bad they were not repairable and they had me make new ones. I talked them into putting them on permanently and they agreed.
Another option if there is enough space with the sink is you could put some wood to the side of the opening and put soap trays on false fronts and they would just fold open with a plastic tray on the back side of the front. I believe the last time I bought some it was about 17 bucks at Lowe's for two trays and two sets of hinges. If they weren't 3/8" lip doors the hinges would mount right to the faceplate but I think you would need wood on the back side with your doors.