You can, mate.
As long as it's not a commercial activity (i.e. fisheries) its perfectly legal to rehome carp and koi etc. Obviously can be risky due to biosecurity but perfectly ok legally.
Edit: They're basically pets so same rules apply.
A real good 10mm cork ball will be ok but it's tricky to get really good cork balls nowadays. It's a lot safer bet using 12 mm cork balls for a 14 mm pop up.👍