1995 issue date

I believe this coin only exists with a 1996 issue date. Is there any pictures of a 1995 in existence?

Some googling around suggests you're right.  There is a Star Trek 1995 coin, but it's Kirk and Picard 

N#79373

Can the 1995 holders be moved to 1996?

They can.

If you post a topic in this forum: https://en.numista.com/forum/forum37.html

When you create the topic you can select the topmost checkbox to indicate it's about the modification of a piece of exonumia

Then you can explain what you think should happen (ie. users of 1995 should be moved to the 1995 kirk/picard coin) and see how it works out.  Be sure to post links to both coins.