I'm glad you didn't try to pull the wool over my eyes.

Brilliant deduction, Jackie.

"Pulling a fast one" refers to the mugger's practice of pulling the wig ["the wool"] over the eyes of the 'mark' whilst the mark is relieved of his valuables.

The mugger disappears into the crowd leaving the 'mark', like a fish out of water, to re-pate-riate his dignity.

[Little wonder the wig fell out of favor.]