Joanne wrote:

Last autumn, I planted two conkers in my tiny back garden, just for the fun
of it. Of course, both conkers sprouted and now I have two little
horsechestnut saplings. Obviously I can't have them in my little town
garden, but I don't want to throw them out.

I'd thought about transplanting them in a little nearby wood, but I don't
know if they'll become a nuisance (possibly causing some poor
future-generation child to put out its eye when playing conkers without
wearing safety goggles).

So, should I transplant them or simply bin them?

Did you plant them straight in the ground?
If so, why don't you transplant them in a pot and keep them. Restricting
the roots will keep them quite small. I have one in a my small garden in a
20inch pot - it's over 10 years old, about 1.5m high.