Maybe mention to them that if you die, you just get a free transfer off to one of the other servers. My partner was pretty HC adverse until I pointed this out, then she was happy to play HC. We made it to about level 25 or so and biffed it to a spider chain pull in Duskwood (as one does). We transferred to Mankrik and happily continued playing there 
Yea, just don’t trade with others. Or only with each other, which could be a fun way to play. If it’s a question of willpower, that’s where having a dedicated mode certainly is nice, but at the end of the day it doesn’t matter much. These challenges tend to be for people who are already very experienced at the game, to provide a little more flavour to the journey. For those who aren’t experienced, they aren’t really necessary, and for those who are they tend to be easier to stick to.
It would be nice to have support for this on the live servers, but it’s easy enough to just do it yourself. Either way, good luck to you and your friend!