Trying to recover data from water damaged 4s

I'm trying to recover the data on a water damaged iphone 4s. I completely cleaned this phone and replaced battery. iTunes does respond when this phone is plugged into a laptop,

But I can't get an image to appear on the screen, most likely a blown LCD filter (I have the logic board plugged into a screen and LCD that are known to work, not the one that was on the phone when the water damage occurred). Don't want to mess with trying to replace that so decided to try to pull the data off the phone and transfer to a new phone.

I've tried some of the data recovery programs but have come against a roadblock that I haven't; been able to get around. When using these programs, the program begins to scan the phone, but then a message appears saying that I have to "trust" the PC in order to continue the scan. Apparently this can only be done by hitting the "trust" button that appears on the phone screen. Well, I can't see this trust button because the LCD isn't working. Is there a way that I can bypass this? Any ideas or solutions will be greatly appreciated.