It feels natural for me to pronounce words like "paths" with a slight "z" sound at the end. Others close to me do not. What sort of accent am I mimicking? Or, am I making up my own accent?
There are many English words in which a final voiceless spirant (usually /f/) becomes voiced when the word is pluralized:
(This goes back to an Anglo-Saxon intervocalic voicing rule.)
What you're doing is applying the same rule to words ending in -th, changing the voiceless "th" sound [θ] to the voiced "th" sound [ð]. However, since these two sounds are spelled the same in English, most people aren't aware of this alternation, and the words that alternate in this way are not marked in dictionaries as irregular.
FWIW, I also pronounce "paths" as [pæðz]. Some other words that show this alternation, at least in my dialect:
What you are describing sounds like "regressive voicing assimilation." Usually when forming a regular plural, whether or not you use an -s or -z sound depends on the voicing of final sound of the word.
-z goes with voiced final sounds, and -s goes with voiceless final sounds.
But, there is also a number of words for which you add a -z and change the voicing of the final sound of the word instead. (examples from The Handbook of Historical Linguistics by Brian D. Joseph and Richard D. Janda)
As you can see, most of these involve f -> v. But there are a few that have the -th sound. There isn't a way in the written language to represent a voiced -th, so I'll used -dh here.
For a lot of these words, there is dialectal variation, and individuals probably vary also. I believe that "paths" is recognized as being in variation, since the Merriam Webster online pronunciation provides both "padhz" and "paths".