You can use the skewer that comes with that bike on the Hammer -- I have that bike and I have mounted it to that trainer with that skewer. Getting it started is challenging because as you noted the lever does hit the trainer, but it is possible. It is easier, however, to use a Kintetic thru axle adapter instead so you can just spin it on using a 6mm allen wrench. Make sure to get the Traxle Coarse T-2101 version.

Thank you SO much, cyclingguru!

For any idiots from the future that cannot find any other threads on the internet regarding this... cyclingguru's vague response of "it's difficult but it works, try harder" may have you scratching your head. Do not fear, the hidden key is understanding HOW your DT Swiss skewer actually works! I watched a youtube video(link below;58 seconds in) and realized that you can pull out the spring loaded lever-head of the skewer, rotate it backward within your clearance of the Hammer, push it back in and tighten.

You just repeat this 1/4 turn by 1/4 turn over and over and eventually you will have the skewer fully tightened. Note you may have to use your fingers to keep the axle in place while you "Reset" the lever the first several times.

And I used "idiot" jokingly, as I had a big forehead slapping moment as I realized the missing key to all this.

I hit this issue too. I'm aware of the DT Swiss ratcheting action, but the problem is that you can't get enough thread into the other dropout before you have to start ratcheting. The solution was to wedge the TA in the bike frame while you get that lever back around. I did it once. It wasn't fun.
I found a Cycleops 12x1.75 thread trainer skewer (for the wheel-on trainers) 1/2 off at PB's going out of business sale. I'm going to try that. https://amzn.to/2R6r9Ur