Letting your shorts dry for the 8 - 10 hours you're at work, then putting them back on again to ride home isn't going to cause fungal infections. Seriously, I spent 11h 10m on my bike last Saturday; I wore the same shorts for the 1h drive to/from the starting point, and I didn't change during the ride. We got rained on, and I was sweating for most of the time. No infections.
BTW, XK-12 sanitizer, Brunswick sanitizer, etc. are just ethyl alcohol with an isobutane propellant and some fragrance. You may as well just splash your junk with some Everclear, spray dry it with canned air and give your undercarriage a spritz of air freshener.

Bike shorts are all the support you need. Actually, padded cycling shorts are specifically designed to be worn sans underpants. The lycra material offers the compression and support normally provided by something like (ack!) tighty whities, and the chamois padding in good shorts is wicking and breathable to keep moisture away from the body, plus many are manufactured with antibacterial cores or antibacterial threading in the coverings. Bike shorts are also manufactured with anti-chafing flat-locked seams, and panel seam placement designed to be at the least irritating spots. Tighty whities have rolled seams which will cause irritation/chafing; plus they're usually cotton, which will get wet and stay wet against you. If you're on a very long ride (say, 6h or more) you'll likely be using a chamois creme if you're freebagging it in cycling shorts. Most of these are also designed with antibacterial agents as well. So it's one more boundary of protection from problematic bacterial buildup.