That's a tough one. If you're avoiding bug spray, then covering up is probably your best bet. Not ideal when running in the heat, though.
FWIW, if you're using bug spray that has 25-20% concentration of DEET, it's pretty safe. Some people can get some toxicity, but that's usually from misuse (e.g. don't over do it, don't eat it, etc.). It's so widespread and has been used for so long that if there were problems, we'd probably know by now. I say this as someone who is also trying to minimize chemical usage (shampoos, PFAS, etc.).