Used a 300 win last year on a nice Tn whitetail, damage was not excessive. Ive killed several with the 7mm mag and it is probably my favorite overall whitetail round to be honest. If you are comfortable with it, take it and go hunting.
I had some of my preconceived ideas about using "too much" gun laid to rest when I was shooting deer with 200 gr. accubonds out of my .325 WSM. I found that using a bonded bullet and a big caliber left far less bloodshot meat than light bullets out of medium calibers. I wouldn't recommend using a "big" gun with a hot load and light bullets but I'd shoot deer with your set up without hesitation.