If going by public transport I cut down on non essentials but I still take my debit card, normal phone & punting phone, cash for punt and a bit more. Yes, mugging, getting ripped off etc are a risk, but I see it as not as bad as getting stranded miles from home with no dosh, especially if you're not supposed to be there!!! It helps if you've done your homework with the WG too.
I don't take a wallet, just hide all the items around my pockets and of course, if showering take it all in with me.
As has been said many times, if you considered every single risk, you wouldn't punt, all you can do is take sensible precautions.
A big risk and something that has happened to me a couple of times is meeting someone I know on the train, helps to have a cover story ready.