Shower with the baby

Oom

My partner wants to take a shower with our 9.5 weeks baby, but I don't like the idea at all, as she is still small and can't control her head yet. He would hold her with one arm and cleaning her with the other arm. The soap could make her slippery, the shower would run through her face while washing her hair. I see the risk of dropping her. Am I over protective?