I don't know much but didn't want this to go unanswered!
I imagine this happens a lot and there is absolutely no problem with a child being baptised with only one parent. You might need to confirm dad is not involved, or if he is, that he has given permission for baptism because it wouldn't be good for baptism to be a covert thing or a cause of argument between parents.
Talk to your vicar/priest about the wording and register. In the CofE I think the only word to change would be 'parents' to 'parent'. Mums and Dads are not addressed individually. The Catholic rite is very similar so it may be the same singular/plural adjustment.