hello Neil,
well in short... no you cannot use the charger as a power source for the lift. They both run on different frequencies for starters, the amp draw from the lift is something the charger is not designed to withstand. Most of the time when a charger is plugged into a lift bad things happen like logic meltdown's etc.

secondly if you want to modify the lift with a remote it generally is encouraged and in most cases instant to call the mfg of the machine to get approval on any modifications.

Now from what you have described in your operation a lift truck might be a bad way to handle the product, in your application you may be better going with a lift table or conveyor lift. The reason i suggest this is for safety sake and safe product handling and operator safety.
I deal with a company that has all sorts of these and can even custom build one to your specifications.
h t t p://w w w.southworthproducts.com/content50.html

^^^^^^^^^^ remove the spaces i added in the link or just google southworth.