Books bought through the iBooks store will not be a problem. You can just download them again if something goes wrong.
PDFs in iBooks can be mailed.
ePUBs that are not from the iBooks Store are a problem. I don't know of any way to strip them back out of iBooks. You can try the Transfer Purchases method, part of the procedures I'm going to paste below; but it often does not work with non-iBooks books.
Hopefully someone else has something that will work.
If most or all of your ePub files were free, then I suggest making a list of them so you can go find and download them again, just in case.
Otherwise, the below method should allow you to connect your iPad to a new computer with a minimum of losses.
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Here is Apple's recommendations on how to transfer all your stuff to a new iPhone. With a few modifications it works very well for moving your iPad to a new computer. Wish I could find one as well written for the actual task.
iOS: How to back up your data and set up as a new device
Start by going into iTunes Preferences (before connecting the iPad) and turning off auto-sync. It is under the Devices tab. This will prevent any unwanted syncing before you are ready.
Do only the parts that apply to your information/situation (i.e.; if you are syncing contacts with Google, don't do the Personal Information Manager part. Stop when you get to the Restore step.
It would be wise, after the Transfer Purchases option to go through iTunes and make sure everything (media, app, book) got transferred. If not you may have a few more steps to insure all your stuff gets safely backed up on the computer.
NOTE: If you have picture albums in the Photos app, and they are not backed up somewhere other than the iPad, you need to save them first before doing anything else. The first sync will remove them. The PhotoSync app works well for this, and you can use it before starting any of the other procedures.
The quality of the pictures recovered this way will probably not match the originals. iTunes optimizes photos for viewing on the iPad when it syncs them.