Block is honestly less mandatory than you think, but the real bottleneck on Switch isn't perks - it's gear and enchantments. You can absolutely tank without sinking into the Block tree if you're willing to be a bit more active about it.
Light Armor + Smithing is the way. Get your smithing up early, grab the perks that boost light armor rating (the ones that reduce weight and boost defense), and stack whatever enchantments you can find - especially stuff that boosts armor or reduces incoming damage. A well-smithed set of, say, steel plate or elven gear will carry you way further than people think, especially if you're matching pieces for the set bonus perk in Light Armor.
The real trick though: you need to actually use your shield. Not for blocking (which sucks without the perks), but for bashing. There's a perk in the Block tree called Power Bash or something similar that staggers enemies when you bash, and honestly that one perk alone is worth grabbing if you're not going full tank. Stagger is your mitigation. If enemies are on their back, they're not hitting you. You don't need to tank hits if they're not attacking.
Also grab the perk in the One-Handed tree that increases damage with one-handers - I think it's Bladesman? - and maybe the one that lets you swing faster. You're going offensive-tank, not passive-tank. More damage means shorter fights means less damage taken overall.
What difficulty are you playing on? Because on lower difficulties you can basically ignore Block entirely and just wear decent gear. On Legendary it gets spicier but still doable.