Is there any rule (of thumb, I guess) prohibiting me from wearing any tartans that I may be related to, though not directly (i.e. blood relation)?
The short answer is "no". There is no rule against you wearing the tartan of a family whose blood runs in your veins, regardless of whether you carry the surname or not.

There are some people (and thankfully they are few and far between) who insist that one is only entitled to wear the tartan for a clan whose name they carry, but this view is historically incorrect and is nothing more than a lame attempt at snobbery and elitism.

It's generally considered good form to wear only one clan tartan (such as they do in Scotland) that you are connected to most strongly. But still, there's no rule against it.