Wire around the switch and put the power plug in a multi outlet with a switch. Turn the machine off and on with this switch! Also plug a couple of lights into the multi outlet, so they go on when the lathe goes on.
I agree with the idea of replacing the built-in switch with an external switching device, but I have an issue with the concept of having the lights come on only when the lathe is turned on.
Lathes are switched on and off frequently, and when the lathe isn't running, the turner is usually either doing something to the turning, or else inspecting it closely to see what needs to be done to it. This requires light. So I think the lights need to be on all the time, not just when the lathe is actually running.
My lathe is plugged into a block of outlets that are set up with a master switch. I also have the lights over and around my lathe plugged into those same outlets so that when I close the master switch,
power is available to the lathe and the lights all come on. But then I can switch the lathe on and off independently.
One other thought - I've seen a lot of reports about switch failures on the Delta 46-460 (and also on the Turncrafter that I have although mine seems to be OK for now). The frequency of these complaints leads me to wonder if the switches that are used in these lathes are robust enough for the duty they get. There are also reports that getting replacement parts for Delta lathes is sometimes difficult, and I suspect that retrofitting something other than an OEM replacement would be problematic. So substituting an external switch does seem to be the right answer, and that approach also means that its possible to use something more rugged.