First of all, relax and enjoy the trip and dont over think it too much. I assume all of the RS family are quality folks and if you travel as you live you cant do wrong. But its a fun subject to pick on so forgive me.
You don’t need shorts to give yourself away.
In Budapest you will look like a tourist if you are a couple and it’s a weekday between 8am and 5pm you are standing in front of the Opera House, or the Parliament or waking through the Central Market, or taking the tour of the Great Synagogue or wandering across Heroes’ Square, or traveling the M1 Metro or shopping on Vaci utca or speaking a language other than Magyar … or asking, “what is a Magyar?”
In Prague you will look like a tourist if you are in Old Town and you are not serving tourists.
The downside of looking like a tourist? There really isn’t one. But you do get to decide what sort of tourist you wish to portray yourself to others as.
I think those picking pockets are criminals of opportunity. They go for the easiest prey despite whether they are local or tourist. If tourists get hit more, it’s because they are the most careless or in the most opportune locations such as packed cheek to cheek in Prague Old Town or the Charles Bridge. But I also suspect that a sizeable number who claim they got picked just left their stuff someplace and forgot. In 25 years of coming or living here in Budapest I have never met a person who was pickpocketed. Never met a person who knew a person either. But I presume it does happen.