[Goober]

Are you sure you removed the CDI and not the adjacent overheat alarm box?
Ill have to take a pic of my ‘95’s CDI can’t remember what it looks like

 

[Goober]

TE15E-85XXXXX as best as i can tell is a ‘93 engine and they do not use the same CDI.
Your connectors should be the same, so that’s odd.

 

[Goober]

Here’s a link listing your engine as from a 93 TRX300FW

Honda Starting Frame VIN Number and Engine Serial Numbers | AtvManual

Below is a lookup table to identify the make model and year of your Honda ATV. This data covers all ATV models from 1973 to 2000.

atvmanual.com