Hooked Up Mower Battery to Wrong Terminals?

I did a very bonehead thing. In the fall I disconnected my standing mower battery, as I should, neg (black) first, then positive (red). However over the winter I did not remember how the battery fit into the slot. I put it in, as I logically thought it should go. However, I did not confirm neg to black, pos to red, I just used the cable lengths to "logically" put them where I should.

So, I then managed to hook the the red to the neg terminal and the black to the positive terminal. Now that I recognize my problem, I am not sure which to carefully disconnect first. The black cable on the positive terminal, or the red cable on the neg terminal. There were a few sparks.

I know you are rolling your eyes, but I do not want to harm the mower.
I am going to go and try putting a rubber mat under the terminal to cover the locations that would spark, wear gloves, and move very slowly, so as to not cause a spark or shock myself or hurt the mower.

Needless to say, I did try to start it, even though I could not close the battery compartment (first sign) and it would not start. I hope I did not hurt it.

Thank you for any help.
"feeling like a bonehead"