Can a woman go into the trades without being sexually harassed by male counterparts?

Yes, and it's even much better now than it used to be.  I'm not saying that there's none, nor that some workplaces aren't worse than others, but once you get over the hurdle of proving yourself for the most part the banter you'll be subjected to is no worse than that between men, but if you've never worked in an almost exclusively male environment before you may not realise just how rough male banter can be.  It's a different dynamic though and once you're accepted you're "allowed" to give as good as you get.  

Really the worst part IS proving yourself.  Women are still held to a higher standard.  Men seem blind to that, but I've never met another woman in trade or construction generally without tales to tell, not to mention all the palaver of needing to source PPE (personal protective equipment) that fits properly on order to do the job with parity.  It used to be a common ploy to try to run women out by giving us deliberately extra poor fitting PPE sometimes making the job outright dangerous, no to mention when I started out I was more than once told I could not be hired because there was no such thing as PPE in my size.  So, I sourced my own compliant gear at my own expense with none of the advantages of scale when companies buy in gear, and then bullied my way into work.  It did mean that I was paid less in real terms because I was paying for what the lads got given but I did get to prove myself and work my way up.  Things are better for girls now, for sure, but there's still room for improvement.

Still, it's better than waitressing or cleaning.  I hate to say it, but those roles have a cultural power imbalance built into them whereby even nice-seeming people on the surface harass staff because they can socially get away with it and they take out their frustrations on them.  Those men harassing you didn't do it because they were "just paying you a compliment," you can feel the nasty edge in the way they do it.  In trade you have the respect of the work itself.

Only if you allow them to...if you challenge ANYTHING that is said that is inappropriate, with confidence and directed to the person saying it.... males grow up physically but mentally they remain silly little boys and silly little boys like other silly little boys around them to show off to.... stop treating them as mentally grown up men, talk to them how they are behaving like a parent to the silly little show off boy they are

Just by dressing appropriately for the job should reduce the amount of comments to the minimum. 

From experience and knowledge, most guys deep in their hearts want women to succeed. We're a little leery that we'll be misunderstood as it is usually new to us too.

If a woman goes into the trades or an 80% male environment she's probably a lesbian.

I work in a ware house and I've never been sexually harassed by a male co worker. If that's happened to you, you should report it to your boss. Even when I worked in retail that never happened. 

It might be worse if you worked in a mostly male environment. 

If you are going to get all hurt about this type of stuff anytime it occurs, you should probably just stay at home doing nothing.

As a woman, I don't care when people mention this type of stuff.  Talk about my girls, if it makes you (ie. the person talking about them) pleased or happy to do so.  I'm not so out of touch that I don't realize that they are "right there".  If you are so stupid to not know or not care that it's inappropriate that really doesn't have anything to do with me.  Nor do I read into stuff -- if someone says something positive about my physical looks, I take it as a compliment not that they are trying to get in the sheets with me. 

These things happen in all businesses.  I work with a VP in a big company.  He loves to open the door for me and when i walk through he lightly directs me through as he sweeps his hand along my back bra strap.  It just makes me roll my eyes. 

Women claim sexual harrasment very often for some sort of monetary or career gain. Situations of actual sexual harrasment are much more common when those conditions are removed. The reason is women will get pissed off if they feel they can't get something out of the situation with a guy and other men have a tendency to want to play the hero. So in other words was Cuomo willing to go public with that younger woman and giver her half of his money for sex? Or was he concerned how taking that approach would ruin his political image because of her job?

Well  it all of them are matured in  a proper way.  Wait a minute even the ones in   government and  the ex-president is not like that..... So NO is the answer.

Depends on the job, who is running it, the shop so to speak.