How to do that on a much smaller scale e.g. when I have only 3 servers available? If I deploy to one of them potentially 1/3 of customers might get broken version.
You don't have to have all three servers getting the same amount of traffic, and you don't have to have a single copy of your service on each server. So, you could reduce the weight of a single server that does canary traffic to reduce the pain, or you could run two copies of your service on a server, and have the canary copy get a trickle of traffic.
Another approach is to use shadow traffic - instead of handling the requests on the canary host, you handle it on the production host _and_ the canary host. You'd need to ensure the canary can't adjust the production database, for example - or maybe you only shadow read requests. If you don't get any errors, or you're able to prove to yourself that they function the same, you can then move to a more traditional canary.
You definitely need to adjust your continuous deployment implementation to your environment, whatever it is.
1) Add 4th server at new version
2) Drop 1 old version
3) Launch 1 more new version
4) Drop 1 old version
5) Launch 1 more new version
6) Drop 1 old version
This way you never have less than 3 servers serving requests, but you never pay for more than 4. Should only cost a few cents for most cloud providers for this temp server.