[latch]

Just be upfront about your situation in your cover letter. It'll save everyone time. Put it in your first introductory paragraph.

From my limited exposure, it does seem like most companies are willing to sponsor for the right candidate. Even small startups seem to have the capability to do so.

One thing to keep in mind is relocation costs. Larger companies will often help with this. Smaller companies might expect you to carry this burden yourself. You should figure out the cost and figure if you can cover it - if not, this is something else you should be upfront about.