If it's not on IGI or the Isle of Man Family History website, there's no way you could check for a middle name online. The only way is to come to the Isle of Man and look at the Rushen baptisms on microfilm, or more practically pay a local researcher to do it for you. As you have a reasonable idea of when he was born, then it might only take half an hour.

Contact me via e-mail if you can't find a volunteer and are willing to pay a modest fee...

david(dot)radcliffe(at)manx(dot)net