It's ok to send it to an Exchange, well I'm my case it is Volabit ( not sure if it's considered an exchange).  I just let the BTC accumulate there until I get like a 0.5 or 1 BTC and then I transfer them to the hardware wallet (if I don't sell them right there and then).  I think it is completely fine just don't keep too much BTC there, I personally don't let it go over 1 BTC.  For me Volabit works the best, I like the page layout, notifications and they charge me barely anything for pulling my BTC out.  I've never had a problem with any of the transfers from them, and it Has been always very quick for me!