Hi!
You can transport your units using riverine movement if you hug to the coast. Its slower but doable.
Just beware to not pass by any confederate fortress on the way and to protect the area with some ships. From Washington DC to Fort Monroe (best start up location for a Peninsular campaign) the way is clear and the small CSA navy is not a danger. So you can do it easely
For expeditions down the coast it's better and faster to use real transports.
In any case, each transport can carry half a division so you don't need that many.
Besides, these ships are cheap, can be used to build depots and give supplies and stationed on the Shipping box gives you lots of money ans war supplies.
They are agreat investment! You can't have too much of them!
Regards!