I highly recommend using paper until everything is healed up, as mentioned earlier. I simply can't comment on the cardboard under the paper because I wouldn't ever do it that way myself. I never set up a heat mat without a control first and can't/won't guess at how well cardboard might work. I will say that if you choose to do that, you'll have to be sure to have enough of it to change it out every time he poops or pees.
A little spritzing on the substrate shouldn't hurt...but if it's WET, then that could be an issue. It won't hurt to let the humidity drop a bit during this healing time. In the 40's would be alright...then bump it back up when you see him getting ready for a shed. (Which may be fairly soon, as wounds/injuries will often induce a shed)
Thank you! I meant to mention that and forgot to include it. Please don't use tape in the enclosure. Very dangerous!