You sure about that? Or is it that the majority of women don't see themselves unclogging toilets for a living? I have never seen it, but I would suspect list of female applications to plumbing or electrician school is very very short.
Few female applicants to trade schools is consistent with the original statement. If it is societally unacceptable for a woman to be a plumber then I would expect women to act as any rational agent and factor this in when planning their future career.
As for your claim that higher class males avoid trades: yes of course. That is actually a great example of what I mean. People factor in social norms in their decision making, be it male or female.
I believe that norms shape behaviour, that is the extent of my claim.
But like, given they require physical strength, it is hard to make a big deal about it.