The only reason you need a rooster is if you want fertile eggs. Anything else is personal preference. Some people are extremely happy not to have a rooster with their hens, others wouldn't want a flock without a rooster.
With Isa's and leghorns you'll probably need an incubator to hatch chicks as neither tend to go broody. If you did hatch chicks, what would you do with them, males and females, eat them, sell them, give them away, or keep them in your flock? We'd need to know what kind of cockerel that is before we could tell you what genetic traits he would bring to the table.
A true meat breed like a Cornish Cross tend to get huge. Often they have medical problems as they tend to outgrow their heart's ability or their skeleton breaks down. With your comment about white chickens for meat a Cornish Cross is a real possibility. This could be a genetic throw-back as far as feather color. They want all-white birds as the darker feathers can mess up the carcass's appearance when they are plucked. But that is only a guess, it could be White Rock or something else. At five weeks size is a good indicator.
Your hens tend to be fairly small, a Cornish Cross cockerel could get massive, maybe too big to breed. While a hen can handle a rooster that weighs a lot more than she does because she squats on the ground when they mate and transmits his weight into the ground through her body instead of through her legs, the more difference in size the more risk. That just might be too much. If it is a Cornish, you might need to house him separately and keep him on a restricted diet to keep him from getting too big.
It's stuff like this that shows why we need to know a lot more about that cockerel before we can tell you what the results could be. If he is a dual purpose bird the size difference should not be a big deal. I just don't know.
