Sorry I have been a little late to reply on my experiment. I have ordered the Dell Active Stylus (750-AAGN) available on Amazon for approximately $25 USD. You can read up on the reviews on Amazon and the issues reported in this Dell community support forum. (Sorry I cannot post links as I do not have enough post count).
So does the pen work with Dell Venue 8 7840? Well...it works...kinda.
There is some lag between pen stroke and before the stroke will appear on screen. Certain apps are worse than others. Sadly, OneNote Android version is so poor that it is simply unusable. Lag with LectureNotes and Squid (also known as Papyrus) is useable...but there is still some slight lag when writing fast. Autodesk Sketchbook is actually decent. However, I don't feel like the Android driver truly supports 256 levels of pressure sensitivity. It seems like it may only support 3 or 4. It usually writes bold lines and not thin lines.
The stylus uses AAAA format batteries which are troublesome and somewhat expensive to find. The problem seems to be that the stylus eats batteries on standby. After the battery has drained somewhat, the stylus has significant problems connecting with the tablet. So you need to be prepared to disconnect the battery after everytime you use the pen or buy rechargeable AAAA batteries (which is what I did) and keep or carry around fresh backups with you.
If you can deal with the battery issue, this is a surprising bonus accessory for a tablet did not say it had pen/stylus support from the factory.