Buy some light weight leg warmers or knee warmers might just do the trick. Your lower part of your calf and ankle would get some sun, but you might be able to live with that with knee warmers.

The castelli knee warmers are pretty light weight, they might work for you. I know they make cool arms to keep sun off your arms, but I have not seen the equivalent in cool legs.

The leg warmers just go under your short at the very bottom, so they do not affect your shorts in any way up top where you really need the comfort.

spoke