Searches that exclude particular transit airports

I need to go from YYZ to SIN, but this is a more general question about how to work the various search engines most people use. There are no direct flights. There are plenty of 20 hour flights through Hong Kong, but it has been suffering some event-based-effects that have, in the past, involved the airport, so I would rather not connect through there. There are a few through Manila, but it's having a volcano and I don't know how long that will last. And other possible transit points are problematic, I don't want to list them all.

I can restrict my searches to one-stops; I can sort by duration; but I don't seem to be able to say "I can't transfer through that specific airport." I could set up a multi-city trip through the one airport I am willing to transit through, but there are probably a dozen airports I'm willing to transit through. This search capability might also be useful to people who have transit visa issues and might not want to go through a specific country for that reason.

So, is this a service some search engines offer? How can I do it?