I knit all the time with the regular Addis, but I want to say (I’ve tossed out the labels, so I can’t check) that at least some of my pairs don’t have the nickel plating.
I think a couple them do, and I haven’t had any trouble with any of them. Do you have anyone who has any that you could try for a couple of hours? I know it sucks to risk the rash, but it’s something to consider. For one thing, when you’re actually knitting, particularly in the round, most of the time you’re actually gripping yarn and not the metal.
You could also try the clear fingernail polish trick. I wouldn’t put it up at the tips, but on the shaft of the needle, where your hands go, as long as you just applied a very thin smooth layer it might work.