Lots of thoughts, obviously see your doctor, etc etc etc
Stay away from boots, look to ultra-light / light trail shoes.
Look to some of the newest/highest tech footwear. Light hiking shoes and trail runners are evolving very quickly with lightweight and breathable materials. For the most part staying away from Goretex might serve you well but there may be some exceptions.
Look to lighter weight socks to go with the lightweight/breathable shoes.
Expect to spend a few bucks on the shoes, the newest/lightest/most breathable styles are not cheap, but might be an excellent investment.
You may find this very interesting, from Backpacker Magazine, their Editor's Choice award winner 2015,
the video specifically talks about sweaty feet! =>
LaSportivia Synthesis is available in mens & womens:
http://www.backpacker.com/gear/foot...editors-choice-la-sportiva-synthesis-mid-gtx/
Their 2014 Editors Choice winner was the
Zamberlain 230 Crosser GTX, which is a light hiking boot. I would avoid the Goretex boot,
but they make a NON-Goretex hiking shoe, the model number is the 129 Crosser. I personally own both the 230 light boot and the 129 light hiking shoe. If you are looking for a durable light hiking shoe with plenty of shock absorbtion and plenty of toe & foot protection, then seriously consider the 129 Crosser. Its light, and it breathes far better than the boot version . . . but not as light, and probably not as breathable, as the trail runner type shoes. It is available in both mens/womens versions.
I'm not overly fond of
KEENs, but I have a couple pairs. I find them to be very stiff in the sole and my feet tire quickly when using them but perhaps some of their "hiking sandals" would be suitable, and clearly far more breathable than most any shoe.
Teva and
Chacos are alternate brands that have hiking sandals. I also have a pair of Tevas but don't have any experience with them on trails.