Edit Mode bmesh script.
Tested on subdivided and poked cube.
Tags all edges that have a face angle > EPS
Gets all triangular faces made up of only edges not tagged and joins them. (To Quad)
Feeds all verts that have no linked edges tagged into bmesh unsubdivide operator.
Can edit properties of both to quads, eg max face angle, and iterations for ...
Is there a better way to import the files that will give me a cleaner mesh?
This is less a Blender question at this point than a Sketchup question; The import isn't making all the tris, Sketchup is. Perhaps see if there's a "quads" export option.
Assuming that isn't an option (because if it is, you can stop reading), you have two options;
1: Retopologize ...
No reason an edit mode bmesh cannot be used with edit ops.
I prefer NOT to use the BMesh module, since the bpy operators suit my
needs much better.
They are not mutually exclusive.
In answer to
1) For every vertex in object 1a) Select this vertex (v.select = True)
1b) Select neighbor vertices (bpy.ops.mesh.select_more()) 1c) Store
Thanks to a hint from @batFINGER, turns out the best solution is simply to select an edge (Edge Select mode) with no face angles, go to Select > Select Similar > Face Angles. Then go to Face Select mode and un-subdivide.
No scripting needed. For simple shapes, Dissolve Edges will work way better. But beware of face-groups that are selected and connected to ...
I studied your file and I see there are quite some edits you have made on the metarig. Just for comparison, here's your metarig:
And here's my version, where I only added the Cat metarig (edit note: you used the wolf rig, a little different in the names but that's not a big deal) and moved its bones around to fit your model:
(Note I hid the facial & ...