Not certain that the following will work, but as there appears to be no software setting that will disable the touchscreen (understandable as they were not meant to operate without it) you could try disconnecting the digitizer from the mainboard and see if it still works. It may not as perhaps it does a check to see if it is there. You can only try and see.
Here is a link to the Ifixit guide on replacing the LCD screen. At step 9 in the procedure it shows the removal of the digitizer flex cable from the systemboard. Try disconnecting the cable and then insulating the cable end and the connector as best you can to prevent problems in the future and see if it does what you want with an OTG setup.
Just thinking that it may not stay on for as long as you'd like as the tablet will be supplying power to the mouse (and keyboard?) and I think that you cannot power the tablet separately whilst doing this.
Would it be better to try and use a BT connection for the mouse/keyboard and save the power for the tablet/BT? Just a thought.
Nexus 7 Display Assembly Replacement
Not certain if this works or not, again you have to try it and see.
Connect a USB mouse via an appropriate OTG (on the go) cable to your tablet.
This part I know works.
The mouse buttons should allow you to "tap" on selected links etc.
This part I do not know for sure.
Hopefully the scroll wheel will allow you to scroll up and down the page and more hopefully the button on the scroll wheel (when you push the scroll wheel down) will enable the zoom in zoom out function.