Yes, both of those methods are safe.. I don't have any personal experiences of Moneygram but a few years ago I did a couple small withdrawals via WU and everything worked well..
Well it seems most of sites show WU as a possibility and I have used it the pass, but the past week two sites have contacted me and said they cannot accept my deposit even after WU accepted it.
MG turned me down after a review of location it was going to.
Not a clue how to get money into online poker accounts anymore.