9mm is a bit smaller then 3/8" (9mm = .354in, 3/8in = .375) it will slow down the flow rate some and put a bit more strain on the pump, but i think that you'll be alright
The only reason that I can think of that you want to use surgical tubing is if you have to have some pretty tight bends in the tube, but small radius bends also put more strain on the pump and reduce flow.