I’d say it’s a fairly harmless lie, just in the moment, but I’m worried about how it may come back to haunt you in the future. Let’s say you plan to take this farther, and become well known, even just in your local community. Someone will eventually see you with a man.
Two possible “outs” I can see are:
Using the chosen name, but no pronouns, for the child. It can be done if you are disciplined.
Going to your supervisor saying you have an ethical objection to using inaccurate language, but try to work with him or her so that the situation is resolved gracefully. Maybe someone else could take your place and you could work with other children. That only helps the child if everyone else does the same thing (so there is no one available to use the inaccurate pronouns), but it’s better than your using inaccurate pronouns for the child.