as far as code is concerned, you cannot run an individual current-carrying conductor like you would run romex. it is a nuance in the code but basically if you want to add a neutral for this application, you would either need to add an additional cable (romex) or place that individual conductor in a non-metallic conduit (or rip out the 8/2 and install 8/3 (or 10/3 if you went copper)). you would need a #8 aluminum or a #10 copper conductor. an aluminum hot and copper neutral may look weird but not a code violation for a single-phase circuit, provide all the terminations are rated for both copper and aluminum.
practically, what you describe to do is fine and is not inherently dangerous, just be aware it doesn't technically meet code. you'll want to run that new conductor as close as you can to the existing cable along the entire run (another code requirement). separating hot and neutral by an appreciable difference can result in additional circuit impedance and increased heating of the conductors. because the neutral will be smaller than a #6, code does not allow it to be taped to indicate a neutral. you'll need to run a conductor with a white/gray outer finish. another code thing but practically, taping a black conductor is not an inherent danger.
you might have trouble finding #8 aluminum so may want to go with #10 copper. if it was me, i would redo with 10/3 copper but it will cost about $60 or so extra for the cable.