JMO. It depends on your own comfort level and where you will be staying and the places you will frequent. For a work trip where you won’t be in super crowded tourist destinations, it may not be the designer bag that makes you look like a tourist. Europeans wear designer bags too

If you are staying in a secure place; have access to a jewelry safe; are there for work; and are normally a cautious and savvy traveller, it’s your call. DH used to travel very frequently to Europe, and men don’t seem to have any problem with an expensive watch; expensive tailored clothing; leather goods either.
I take carry on luggage and
never check expensive items. For travel, I wear my everyday jewelry (VCA gmop six motif necklace, earrings, watch, ring, but I do not take super blingy stuff like my bracelets and big diamonds — those go into safety deposit box). I wear everyday designer RTW that’s easy to pack, like chanel sweater and brunello pants, simple skirts, flats. I normally take practical designer bags that pack flat; for 2021 trips, I packed a goyard St. Louis; evelyn TPM; and, a men’s Dior saddle. This fall, DH and I will be traveling in Italy for three weeks, and this time I’m going to take my H Della cavalleria mini crossbody. He will probably take a 33 H evelyn sellier, discreet bc no one knows what it is. I did momentarily question whether it was appropriate post covid to take a fancy bag, but I decided, life is short Lol. For my own comfort level, I tend not to bring heavy, bulky or super recognizable bags like a birkin or kelly. If I were to bring a chanel, I pick a reissue. I’ve never had any safety issues myself.
I think you have more chance of being mugged if you look like a tourist, but YMMV.