I don't think it's OK for timidity, as you call it, in either gender.
Both DH and I can sort out spiders - the main challenge is stopping DS trying to play with them! I prefer DH to do it but as he has laughed at me in the past I just do it now.
You have just said that your DH's "femininity" (and I would say it's not good femininity) upsets and stresses you. Surely that means you don't want your son to grow up like this and upset your future DiL? Women are MADE to be protected (don't want to turn this into a religious debate but the Bible says we are), men are MADE to protect us. The world has perverted this, yes, but that doesn't mean that men should be fearful followers and women brave leaders - tbh, women shouldn't be fearful followers either, but men should be leading.
Car accidents are different to spiders though - I know my DH can't cope with anything "medical" whereas I can. That's because he doesn't see it every day, doesn't know what to do. I would have more of a clue but still not enough of one to help beyond comforting and calling an ambulance/the police. But everyday things, the man should be strong and lead.
eta: Mayaness, I expect anyone living in my house to obey my rules. Just as when I live with someone else I obey their rules. Learning how to take instruction is important to a boy and a girl, as it helps when older because they can understand how to give instructions.
OK, so with DS he knows what is and is not allowed (such as don't play near the oven when Mama's cooking, we hold hands to cross the road, we don't re-wire the TV in the middle of Dr Who...) and tests those limits. That's healthy. But he has to live by the rules. Without rules now how will he make them? I don't expect cowering submission but a respectful one.

