You would have to go to Swype's website and see if you can sign up for their beta application. Then if you get invited, download the Swype apk file to your computer, install Android Central Sideload Wonder Machine, follow those instructions to install the apk file to your phone.
You might also be able to find a Swype apk out in the wild, but I don't know where to find it.
When you sign up for the beta, they send a link to download the APK to your phone, but its just the installer, not the Swype software itself. Once you install and run the installer APK, it then downloads the Swype program and does a license check. So I'm not sure how this would all work considering how locked down the Inspire is (only able to install "official" Market apps). But its worth trying. You will easily be able to find the installer APK on your phone after it downloads. So in theory, you should be able to move that to your PC and run Sideload Wonder Machine as previously suggested. But I don't know what is going to happen after that.
There is a Swype clone on the Market called SlideIt. I don't personally known whether its on AT&T's "approved" Market (I'm on the full market), so you might check it out yourself. Its a bit pricey, at $7, but there is a 15-day free trial. Of course, its probably better to have the original real deal Swype. But this might be a decent alternative, if you can't get Swype on your phone.