This depends on your risk tolerance.
Where I am located, most items shipped to the USA take 2 days to leave the Canada Post system and get into the hands of USPS. Canada Post has Monday May 19th off. For USA orders, I would probably use that as a cutoff. If you're less risk adverse, I would use Friday the 16th as a cutoff.
For Canadian orders that are parcel orders, May 16th would be a reasonable cutoff, but you still might get a few stragglers. I use a combination of Canada Post and UPS. Usually, it's roughly the same price for anything non-rural. What I am doing right now is for orders where maybe UPS is a few dollars more, I'm biting the bullet and using UPS. I am only using Canada Post for PO Boxes and rural orders. I'll probably cutoff Canada Post completely at the end of the week.
For lettermail, it really depends on your volume. Most things that ship lettermail are very cheap and have a really long delivery window. I'll keep going with lettermail until the week of the potential strike and then cut it off. If something gets stuck in limbo, sending out a $15-$20 refund isn't the end of the world. Realistically, you should probably stop lettermail this week if you are super high volume where you will have to issue loads of refunds, or you're risk adverse and don't like the idea of potentially having to refund a few orders that don't arrive before the strike.
