At that time of year the winds vary from easterly to southeasterly at around 15 knots about 75% of the time (check the Pilot Charts). Southeasterly would be no problem. Easterlies not so great. Considering you're only looking at about 40 miles, you should be able to make that decision on the evening before your departure. Just pull up PassageWeather.com or SailFlow.com and see what the winds are expected to do for the following 24 hours. With that close a time period the predictions are usually very good. However, why stay in Hawk Channel? If the winds are southeasterly, get out in the stream and get a lift.
"It is not so much for its beauty that the sea makes a claim upon men's hearts, as for that subtle something, that quality of air, that emanation from the waves, that so wonderfully renews a weary spirit."