As long as you can get tool upgrades, hardwood won't be a problem. You can even get 'free' seeds from killing slimes in the secret wood, and ofc you have the stumps there. But if tool upgrades weren't allowed, you can't even access that place, nor remove the stumps on the farm, so that would be a hard lock I suppose.
Suppose the traveling cart is considered a shop and not a service? That makes seeds or random things for the CC much more difficult. It's pretty much a hard block in my own no-farming, no animals game, despite using the traveling cart. The chance for the correct veg or fruit showing up is very small. By using mixed seeds and wild seeds, much is available, but not everything. It's possible to get things in the mail from friendly villagers, but again the chance isn't great, and it could be a big waiting game.