mod doesn't work with another mod that adds skins to minecraft with online mod disabled
link https://www.curseforge.com/minecraft/mc-mods/skinchanger

This looks like an issue with older versions of Skin Changer (and also OfflineSkins, the mods seem to share code), specifically for Minecraft 1.16 and I don't think Chat Heads can be easily changed to accomodate for that.

On newer versions, both mods ASM-patch PlayerInfo.getSkinLocation() (here and here) to return a modified skin, which is exactly the method Chat Heads is using and there is works perfectly fine. Tested OfflineSkins 1.19-v2 with Chat Heads 0.6.2 - just because I had a 1.19 server lying around but it should work on 1.17 upwards as well.
Older versions simply do not have that patch.

Skin Changer hasn't been updated in 2 years and while OfflineSkins is actively developed, they seem to always focus on the latest Minecraft version, so I wouldn't expect them to backport that ASM patch to 1.16 either but if you want, you can try giving them a pretty-please! 😄