I think you'll be as safe as any other day considering that the various Swiss authorities put a lot of effort into safety.
They've also published cautions on drinking plenty of water, wearing closed footwear, drug taking, etc etc.
But, today's the day I now wish I'd planned to get away. I've forgotten how the DOOF DOOF [Australian urban slang for techno or dance music played too loudly - not as in the German meaning of 'stupid', although...] rhythm travels.
I'm 6 kilometres from the Street Parade 'epicentre', I have all windows closed and yet the DOOF DOOF is permeating every millimetre of my private space. And the official start hasn't even begun - and then there's still 12 hours of it. How Swiss I have become. Is there no consideration for us 'oldies', who want a Saturday lunchtime nana-nap?