Take a chance, you'll want to see about getting two bottles...
One of slime, the other of a liquid fix-a-flat.
Here is a picture of the slime:
Unfortunately I can't recall where to get the liquid fix-a-flat, maybe Harbor Freight,
maybe Advance Auto but it's a similar bottle except the stuff is pink.
You'll also need a valve core tool.
Then, remove the valve core and let as much air out as comes out.
Now put a jack under the back of the mower but make SURE it's not touching any parts that would move if it were running!
And get it to where it just starts to lifting, but don't lift it.
Then put the bottle of slime to the valve and squeeze as much of that as you can in there.
Let the bottle recover its air, now raise the mower as you keep squeezing slime in the tire.
Once it's as full as you can get it, re-insert the core, lower the mower.
Now repeat the process with the Fix-a-flat except do NOT lower the mower!
Once that is done quickly inflate the tire with air, start the engine, and CAREFULLY engage the wheel that's in the air
(hopefully both back wheels are in the air).
Run it with wheels spinning for 5-10 minutes to get it all spread out, on mine I was able to clamp the drive
engagement unit down with a vise grip so I could sit back.
Alternatively you could always fill the tire with air, lower the mower, start it and drive it around for 5-10 minutes.
Disengage the drive, shut the mower down (or not) and lower it.
Obviously the above is per tire, I just did this to one of mine as of a week or so ago and so far it's held air.