If you want Lycra shorts for outer wear go to the running section of sports shops.
Other options are swim jammers or square cut swimming trunks, cycle shorts, wresting shorts, or rowing shorts.

and not forgetting women's volleyball shorts:

https://www.adidas.co.uk/techfit-vol...ts/FK0990.html
https://www.kohls.com/product/prd-39...all-shorts.jsp

Lyrca Shorts
 

Well, you can also try the spandex and nylon shorts. But my favorite is https://www.amazon.com/ASICS-Mens-PR.../dp/B00C3LROG2 ... You can check here the more mens underwear styles. Hope you will find your best.

Well, You can checkout at mensunderwearfan.com hope you will found something better.