I really know how insecure is the internet, but not downloading anything and only browser play feels a bit extreme. I think if a game is a virus here it gets reported and take down, that's why there's a community and report system, no? Itch is far from being a shady website. Unless I don't know about some big cases of games being virus here.
I only play the game in the browser if is lightweight, short and arcade-ish, Pico-8 games are the best for this. Otherwise, just download. Edit: Specially browser if the game doesn't run natively on Linux- Wine hasn't failed me that much, but if doesn't run natively, better try on browser then.