"I think any trail that is rated for pack animals and equestrian use is also rated for bike use"

Nope, many trails that are open to pack animals are closed to mountain bikes, as are all trails in wilderness areas. I checked the Wenatchee NF website, and it looks like the upper end of the north side lake shore is within the Lake Chelan-Sawtooth wilderness. The map isn't very good, though, so I couldn't tell whether or not the lakeshore trail itself is in the wilderness area. If it is, it will be closed to bikes.

Good luck with your planning, that's a beautiful area!