I use over-the-head earphones, which can be tightly placed under a hat. No issues of slipping out whatsoever. TBH, they sound tinny and low-quality but like you it's not an issue since the wind and body movement affect the sound anyway, and I know they'll be trashed rather quickly.

Maxell HB-202 Stereo Head Buds https://www.amazon.com/dp/B00006JPRQ/ref=cm_sw_r_cp_api_32k0...