Overhead clearance at Shinnecock is 22ft.
I would do the trip by water and take down the mast just before you enter the canal. ...saves a lot of time and $$ and keeps you in safe water.
You could also simply motor it with the mast unstepped the whole way...but you need to learn to get the mast up and down anyway. Hint...google gin pole!
BTW...my first Catalina 22 was kept in Southold at Larry's Lighthouse Marina back around 1975...small world!