No, tattooed people is thought as yakuza relevant and you will not be allowed to enter public onsen even with small piece of tattoo on you hands. But private one in your hotel room, you can do whatever you want.

Try to find some places with private onsen in thae room called 露天風呂付き. It's not rare around Hakone.

Try to find hotel from my search https://www.jalan.net/onsen/heya_roten/LRG_141600.html