The Park at Cap-Saint-Jacques has several accessible launch points for a kayak.  My preferred one is  here:

Above the rapids, sheltered and parking is usually empty (before lunch).

From there, it’s 40 minutes to an hour (depending on wind and waves) across to Oka Beach. This is probably the nicest beach in the Montreal area. Even on weekends, it’s virtually deserted until lunch time. Bring cash, it’s possible the Park Police will patrol and ask you to pay the entrance fee if you stay on the beach.