It's really just a question of building it right. I think Hack the Minotaur has solo builds on YouTube. As a stamblade you'll want Resolving Vigor and possibly Dark Cloak, which is now a heal. You may want Rally. Aside from that, so many things give you health regen now. For example I run a stamsorc PvP build with Troll King, Eternal Vigor, an Orgnum's Scales back bar and gold food. It tops out at just under 5K health regen (with stamsorc passives) and almost capped resistances on the bow bar in a medium armor build. This is not the only way to go and probably actually too tanky for what you have in mind. It's just one approach.
I made a video a while ago on my stamblade, deliberately gimping myself by only using psijic skills. I took that build into vMA and got through the first 4 rounds. This is a gimmick build, not something I'd suggest you run, but maybe it'll give you some ideas. I use a spammable heal (Crushing Weapon), health regen (Troll King), a 1 hand + shield back bar for blocking and a burst healing set, Cyrodiil's Crest.
https://www.youtube.com/watch?v=fT0T7PzHc3I
If you want to play stamden or stamcro for a change of playstyle, that 's fair enough, but stamblade doesn't really constrain you.