That would be rather dense of him though, and just because someone is sexist it does not follow that they're also stupid
I don't think it's being dense or stupid, more 'better safe than sorry' because I doubt he walks around everyday having to say "needs a man's touch" to a lot of people. To be fair, I think someone who still says 'needs a man's/woman's touch' about anything probably has a shed load of other sexist gaffes they'd think innocent. So for him to "learn to say something different" in place of those words alone doesn't quite get him out of the woods with other possible 'offence' he may cause someone else by speaking to them.
or even just ' stronger hand, glad I could help' would all be fine
Interestingly, I think 'strong or stronger hands' was what he meant there but [I suppose this is where the sexism lies?] 'man/strong' are typically used interchangeably in such cases. [As 'woman/whatever stereotype' is used when someone is happily talking about 'a woman's touch']
So I believe if he said "just needed stronger hands", he'd have gotten the same reaction because it would still mean "You think you're strong just because you're a man and I'm weaker because I'm a woman! REPORTED!"