The WebAssist extensions should not interfere with any existing code or scripts on the site. The tools will create server behaviors that contain the code necessary for that functionality based on the options you choose.
If you need to work within the custom framework you will need to come up with a strategy of sorts for what functionality you want to add into the various areas of the site with the tools. You can then make use of the tools to apply this functionality in a modular fashion.
Please post back with any specific questions that you have about a part of this and we would be glad to help you out with whatever we can.