This would be best accomplished by taking a DNA test with Ancestry.com. The test takes a couple weeks to process. When you get your results back, you can then download the results to your home computer, and then upload that file to GEDMatch,
The ancestry tests are ordinarily about $100, but they frequently run discounts, lowering the price to about $60.
GEDMatch charges nothing to join. If you want to use the advanced tools on the site, there is a $10 per month charge, but the basic tools are free of charge.
As far as I know, WCJD is still not undergoing forensic genealogy, but I suspect that eventually they will. I talked to Detective Bean a couple of months ago. He said they are working on something in that regard, but he did not disclose what specifically they were doing.
If or when they do decide to do FG, the GEDMatch system will be the system used, and if you take the ancestry test and upload it to GEDMatch, the kit will be there for comparison to WCJD and any other Does that are being researched.