I agree about routines. If you are use to completing your checks before taxi (be it for fuel or departure) it would seem safer not to vary that routine. In any event that way at least all the checks that should be done before the aircraft moves are out the way and there is no danger of having left the toe hook on because you were only going to the pumps.
The only caveat is the fuel questions. Draining for water is part of the usual pre taxi checks but I can think of one occasion I was very glad I checked again after refueling having found a significant quantity of water in the uplifted fuel. So that would suggest you leave the fuel checks until at the pumps BUT if there was water already in the tanks often refueling just churns this up with the new fuel and the drain appears far last contaminated than it really is. Also you can no longer "blame" the fueler for his poor quality product! So I reckon it is worth checking the fuel before taxi and after refueling.