[lbschenkel]

I was in a similar situation when I immigrated to Sweden ~20 years ago (I'm Brazilian).

Technically the law says that I'm supposed to carry passport + residence permit (first version was a sticker, then it became a card). However, the hassle of carrying them on a daily basis (and especially losing them!) is too much so I was left them at home. I made a color photocopy of both and put on my wallet instead.

Then later the Swedish tax office started issuing ID cards for non-citizens and I started carrying that (but also the photocopy).

As a foreigner I was not fully complying with letter of the law by doing that but to me the risk of losing my paperwork was far, far higher than being punished for not carrying those. I assumed that in practice if it was something serious they would look me up in the system anyway, or escort me home to produce my paperwork.

Not sure if I that was indeed the reasonable thing to do or if I got lucky, but I never had any problems.