Mike,
Your squeegee handle is made of plastic, no matter how mauch you drop or damage it, it just isn't hard enough to scratch glass!
It might scratch your hand but the glass...not a chance!
In fact, if you dip your applicator in a bucket of sand and wash a window you'll haveto work hard at scratching the glass.
Honestly, give it a try on a garage or shed window of your own, it'll take real effort to mark the glass.
The metal part of your squeegee is capable of scratching glass, and of course you may pick up debris on your applicator that has the potential to scatch the glass, but you will feel it through the handle, you might even hear it!
But as Mike says, there is almost no way you will be able to scratch window after window in a way that is in any way remotely noticable.
Whatever you do, unless you have really really got it way wrong in some almost impossible scenario, don't be bullied into thinking you are responsible for the scratches!!!!!
Ian