@Criggie I did copy and paste the updated question into the original question and as I had expected no one replied to it. Who is going to re-read an original question a second time to get the update? No one. This is ridiculous, I have never seen this in other help forums. It is always that an original question is asked and then if more help is needed then an update is added so people get informed that more help is needed.

Full DIsclosure, I'm not in the US and your wiring systems are strange and alien to me. So use this as no-more than a starter guide.

If you're careful, it should be possible to connect the black to neutral, the live to either Blue or Yellow edpending on if you want high or low speed, and of course you should connect the earth line to the chassis or motor shell.

As a test , clamp down your motor and then plug your lead into the wall and flip the switch, being mindful of all the risks of exposed wiring and moving parts.

Once you know the system turns the squirrel fan, then un plug it and design your housing.

As it stands, a bare squirrel cage fan doesn't move a lot of air. It depends on the housing to control the air being drawn across something.

Also, consider the motor's own cooling. If you're running this for a long time, the motor may need its own cooling.

@Bijan79 does that help ?