Crew Dragon is launching tonight, weather permitting, at about 21:30 BST and ascending into low earth orbit.
It will be flying past the Island about 20 minutes later, but sadly it is unlikely you'll be able see as it will be too light - it you had binoculars and knew where to look you might be able to see it.
But bout 2 hours later it will just be visible from the IOM low on the horizon as it flies by on it's second orbit.
Heaven's above link for Castletown.
See here for more details and a nice video of an earlier pass - the upper stage and Crew Dragon will still be very close together as they go by and so binoculars should resolve two objects [the video shows an earlier mission which also ejected solar panel covers, but Crew Dragon will not have these).