My ds had his op at 14 months but my experience was quite different to Peppa's, guess it depends on the surgeon and the extent of the hypospadias. Ds had a partially formed foreskin but a lot of it so the surgeon was able to reconstruct the foreskin without circumcising.
Ds was in surgery for about an hour. I expected him to be bandaged but he wasn't at all which was a bit of a shock, his penis was hugely swollen and looked very bruised (dh couldn't look!) but he had his nappy as a bit of extra padding I suppose. He was catheterised for two days, which we spent in hospital. The nights were tough as ds found it difficult to sleep, don't think his penis was bothering him so much as the canula they insisted on leaving in his hand.
Once he had the catether out we had to wait for him to wee before we could go home. This obviously hurt as he would just be playing happily and then start screaming - this is the only thing that will probably be harder with an older child as they would be able to hold onto their wee if it hurt, maybe sitting in the bath would help - I'm sure they will have ways of dealing with it at the hospital. The screaming only lasted for maybe half a day and then he seemed fine.
We were discharged with calpol, ibuprofen and antibiotics. Kept up round the clock painkillers for a week I think, although ds never appeared to be in pain once we got home and slept fine. He had 2 weeks off nursery - he would have been fine to go in himself, but I was worried about them changing pooey nappies fast enough as we obviously had to keep his penis as clean as possible. Won't be a problem with a toilet trained child.
Like Peppa, I think the waiting was worse than the actuality! Although the worst bit by far was holding him down for the general anaesthetic and leaving him on the operating table. Apparently the gas doesn't smell very nice, so he struggled quite a lot, and I'm sure it is against every parental instinct to leave your unconcious child to a man with a scalpel!
Ds is 3.5 and toilet trained now and it all looks fine. We are due to go back for a check-up in the summer but I don't think there will be a problem.
Good luck!