You do not need to delete anything in steam there is the ability to move the game install folder.
Right click on the game title in your libaray, click properties then local files.
You should have something like this ( Link ). Just click on move install folder. You will have something like this ( Link ).
Now if you do not have any other libaray location do not worry you can set one up. Just follow the steps below.
So with the client open at the to left click on steam. Then settings. You will have something like this ( Link ). You will see download is highlighted click on that and then click on steam liberies folders at the top of that window. This window ( Link ), will pop up as you can see I have three locations. To add another you just click add libaray folder and you set where you want it. Note if you dont want to use that one a primary thats fine.
You just need to then follow the first part of what I have said on how to movie installed game. I hope that helps.