First, context. Unless you live in a place where a lot of random fistfights/assaults happen, you're mostly only going to be targeted for a mugging - which is primarily someone wanting to get your belongings - not someone trying to waste time beating or hurting you out the blue.
Second, if they are trying to hurt you, while your "hands are your livelihood" the fact is someone trying to hurt you bad enough you need to fight back means you've got things like your life, or perhaps brain damage or hospitalization on the line, all things which will affect your livelihood just as much as a broken bone in the hand would.
All that said, there's many martial arts and self defense courses that focus on palm strikes and forearm blows instead of fists - and that is because even well trained boxers fracture their hands often enough in street fights - so already a lot of people are concerned with protecting their hands in a situation. Based on your question, I'd probably check out one of the many self defense/combative courses in your area and ask the instructors what they feel about fists vs. palm strikes and let them tell you and you can pick from there.
Of course there are many arts with strong kicks and grappling, or even using weapons, but there's nothing that guarantees absolute hand protection - the main thing you're going to want to avoid is the styles with "hand toughening" which often involves striking hard surfaces repeatedly. While this is great for strengthening the bones over long periods of time, it also tends to create calcium deposits in joints years later, which, is not what you want as a career pianist.