Well you've got Sneak Archery of course, but that's the same kind of overpowered goodness as Smithing. But yeah I think it definitely is possible to be succesful on Legendary Difficulty without crafting, but your right it is incredibly difficult, especially as a melee warrior. A mage on the other hand (especially if you can get rich quickly) can be incredibly easy to win on Legendary, at least before Dragons show up, I gave it a shot once (finishing the Alduin fight on Legendary as a Pure Mage) but it's all about dodging and getting your hits in when you can.
I did very well on Legendary with a Conjuration Mage, a Breton for suvivability, I think using vampire armor, necromancer's amulet, Atronach stone, Vokun, and the lovely Jenassa as a follower. We made beautiful dark art together. Killed Lydia and stuck her in the upstairs bedroom.
Do you mean no crafting as in no perking crafting skills, or no crafting full stop? Because if it's the former, Speech is a good replacement for any of the skills, allowing you to buy Fortify potions and enchanted armour to allow for high end gear without perk investment. But if it's the former, then Speech could work, and you'd just buy a metric tonne of potions instead, but it would definitely be harder.
I see that you specifically mention smithing and enchanting would that mean Alchemy (the most powerful skill in the game) is still available? If so than poisons are your friend especially paralysis poisons. Like Dragonborn1721 already said sneak archery is crazy powerful. There is also the Windshear which can cheese all melee combatants, coupled with Spellbreaker and the Block skill and you'll be an unstoppable tank who stun locks any fool that gets too close. Of course getting these two items will be a challenge.
Yes, I've beaten Skyrim+Dawnguard+Dragonborn on Legendary without crafting or any grinding.
It's actually not that hard. You get Teldryn Sero from Raven Rock for a follower early on. You get the Atronach Stone early on. You get the Bound Bow from the fort with the mages early on. You get the Marked For Death shout early on. After that it's rather straightforward. You use Teldryn + a Flame Atronach early on / Dremora Lord in late game to tank and you shoot from distance with the BB. In the instances where you can't bring a follower as well as in boss / hardmob fights use repeated MFD to weaken enemies.