If you're updating Crossover correctly, your installation of e-Sword shouldn't be affected, at all.
To update, first make sure that e-Sword and Crossover are both shut down. Then, login to your account on our website and head to the My Account>My Downloads section:
http://www.codeweavers.com/account/downloads/
Download and install Crossover 10, and choose to "replace" the pre-existing version when prompted.
Now, launch e-Sword in the normal manner. If you've been using a launcher icon saved to your dock, click on that. Otherwise, launch Crossover and then head to Crossover's Programs menu and click on the e-Sword launcher within.
If you're having any problems with updating Crossover or e-Sword, please write to "info@codeweavers.com" and explain what you're trying to do, and what sort of trouble you're having.