Wooster to YNHH is not bad at all on a bike if you take the right streets. You can stay on grade separated bike lanes almost the entire route, but the bits that aren't separated, definitely be careful as others have said

New haven is putting a lot of work in becoming a very bike friendly city with lots of grade separated or protected bike lanes but we're not there yet, but the city adds several miles every year to the separated/protected infrastructure. Last year I think they added nearly 20 miles of new lanes along a few key routes, many more in the works/planning stages