If you check out Skuzzy's new
AH Skins Page you can find out which skins are going to have the shiny problem. Just click on any skin and it has a list of the included files.
There are up to five files in an AH3 skin:
The Diffuse Map is the painting of the skin surface and is not listed on the page because all AH skins have this file no matter how old they are.
The Normal Map simulates bumps and dips in the skin's surface. Later AH2 skins used a bump map to do this job and AH3 automatically converted these AH2 skins' bump maps into AH3 normal maps.
The Specular Map controls the strength of reflections from the sun. Later AH2 skins had this map too.
The Environment Map is new to AH3 and controls reflections from the surrounding environment.
The Power Map is new to AH3 and controls how focussed the reflections are.
Early skins only had the diffuse image file, with other lighting effects either controlled by text files or not at all. These are the skins that have the shininess issue with AH3. Later AH2 skins at least had the specular and bump maps and HTC did a good job of converting these to the AH3 file format. So what you are looking for in order to avoid shiny syndrome are skins on the page that at least have a normal and a specular map, the lack of other two maps does not matter. Also in general any skin that shows a screenshot is highly unlikely to have this issue. However the converse is not true, some skins without screenshots may not have the problem either.
BTW I went into this issue in more detail in this
BBS thread and HT explained what the problem was.