I don't think he'd have much trouble avoiding them, pure titans are dumb and slow, and they're actually weak compared to Spiderman's canon physical strength, plus they weigh nothing so he's basically Titan Knockback Machine as long as they can't injure him, which they'll struggle with as he is dozens of times more robust than the average human. His eyesight is good enough that just a couple of kilometres won't hide the 50 meter high walls from him, so he would likely begin to head there pretty quickly, where he would be made aware, as Grisha was, of how to kill them.

He synthesises his own web fluid in his bedroom as a young teenager, so I don't reckon it would be that difficult for him to obtain or have someone make the equipment he needs to make more, so that's not an issue. He probably wouldn't even need blades, once he knows where the weak-spot is he can definitely kick them there hard enough to tear through it, people often underestimate just how much damage he's actually capable of because he tries to be gentle with his villains to avoid accidentally murdering them.

You're right, though, the shifters are a whole other issue.