I can think of a few ways that might work in theory, all of which would be easy to try if you had a modestly equipped molecular biology lab - but don’t let that deter you, you could possibly get access to one if you start making calls to nearby universities. We used to help out high school science fair types occasionally…
I would try filtering it to remove DNA-containing cells, which would probably get rid of 99.9% of the DNA. There would still be a small amount of loose DNA in the sample due to cell lysis during the filtering process etc, which you could maybe chop up with a DNase cocktail (enzymes that basically chop up DNA). There would still technically be DNA in the sample, but it would be in tiny fragments that wouldn’t be of use for identification. Of course there would also be DNases in your sample, but I doubt a forensic lab would test for those… The minimum equipment would be a vacuum pump/filter rig and filters, a micropipette with tips, some little vials and the DNases, all of which you could order online or rig up at home. DNase itself goes for ~$100-200 for 2000 “units,” which would probably be a lifetime supply for your purposes.
Alternately you could try centrifuging instead of filtering, and the magnetic micro-bead separation kits mentioned above could be used to scavenge any loose DNA instead of using the DNase method. I think this would give you a better “product,” but would require a more elaborate setup and cost more.