There is another way that you could present a " choddie " on mainline without the need for tubing of any kind.
If you thread a rubber float stop onto the line , then a rubber bead with a decent sized bore , then your rig , then another bead , another float stop and finally attach your lead.
You don't have to put the putty on the mainline to counter balance the pop up. All you need to do is mould some putty around the swivel on the rig until it sinks, making sure that the swivel can still spin easily. In theory this could probably be better than lead core as you could balance the pop up instead of it being pinned to the lake bed by leadcore.
If you use a heavy ( in weight ) mainline it should be fine and make sure that you give everything time to settle . If the situation is right maybe use a light backlead to pin things down further up the mainline above the rig.
What ever you do don't put any putty above the float stop as it could stop the rig working safely.
If you do want to use tubing , to stop it slipping up the line on the cast you can either heat shrink it onto the swivel on you lead or use some silicone fitted tightly over the tubing and you lead swivel as well. You can get Tungsten impregnated tubing so you won't have to put all that putty up it either.
Good luck, Seleb.