Just replace the tube; I also carry patches, but just in case of double flats, or to help others.
Incredibly I got another flat today. A small shard of glass. I was 2 1/2 miles out and called my wife to come get me. Which she did.
However, having been shamed here I resolved not to be thwarted and have to rely on a shop. And what do you know, I managed to get the fork off the hub and replace the inner tube unassisted. And I took it out for a 3 1/2 mile ride without incident so hopefully the tube is in properly and the bolts are properly securing the fork back to the hub.
I’ll be taking it out for a 12 mile ride tomorrow morning and I guess that will be a good test.
Thanks aracer - if that really is your name.
I always pull the backing off the vulcanising patches before I stick them on as they don’t stretch like the patch and tube does so can lead to the patch being pulled off at the edges.
I do use the normal vulcanising patches but do also use the park glueless patches to good effect, if the tube is cleaned well at the hole they work very well indeed.
These days I put some agricultural tyre sealant in my tubes and carry a spare (as well as gluless patches to cover all bases.
JJuggle well done, to many that may a seem a trivial thing to do but then what they can do is trial to somebody else so don’t sweat it.
When changing a tube pump it up a little before seating the tyre bead back on this helps to stop you pinching the tube between the rim and tyre and giving yourself another puncture, also worth quickly pushing the tyre bead back and looking that you haven’t caught the tube before you pump it back up.
Use that old tube to practice patching on and keep it as a spare when you go riding (I had a tube with 8 patches that was fine to use).
Well done- repairing punctures is a very useful skill to have, and, it is somewhat tricky to do when first learning.
As feisty says, putting a little air into the tube when putting it back on the rim and fitting the tyre, is very useful to minimise the chance of getting it caught between the rim and tyre when fully inflating it.
That is something I take a bit of care with, as, if a bit of tube does get caught it tends to explode either while inflating, or, soon after- it’s has happened to me a couple of times in the distant past and, it is very unpleasant as it sounds like a gun going off 
So, after getting the tyre on, before hitting the pump, I run the entire wheel through my fingers to check there’s no issues, then pump a bit more air in, check again, put more air in etc, etc. I also give the tyre a few small bounces on the ground between the pumps- not sure if it actually helps, but I’ve seen other people do it and just got into the habit.
(Incidently, does anyone know if the bouncing does help, and, if so, how?)
Basic unicycle maintenance:
Buy the right tools, and don’t buy cheap quality.
Try one job at a time, when you have more time than you need.
Work steadily and methodically.
Remember how things come apart.
Keep loose nuts, bolts and washers in a bowl.
Keep everything clean.
Don’t overtighten. The size of the bolt is a clue to how tight it needs to be.
Ride for a short distance then recheck everything for tightness.
Have a go. Most of the routine maintenance is simple.
If in doubt ask here, there are no stupid questions just people who are stupid to ask 
I probably got lucky. I slide the tube under the half off tire, pumped the damn thing up all at once, and then reattached the fork to the hub. Next time I will pump it up more slowly and attentively.
But I took it out on a 14 mile ride this morning without incident. I’m glad to have obtained a new skill and not have to rely on someone else to fix this minor problem.
Thanks again to those who provided encouragement.
corrected.