I did a bivouac in the opposite mountains (not far from the Bachalpsee lake). You can do without a bivouac but the walk up there is probably around a couple of hours from Grindelwald. You can shorten the walk by using some of the cable cars around but opening time may restrict you in terms of capturing the best lights.
As far as I know in Switzerland it's allowed everywhere except in national parks (there's only one in the Grison region) and some other locally protected zones. But as long as you leave nothing behind then I'd believe you should be 100% safe over there (if unsure just check at the tourist info in Grindelwald).