Replace physical puch button with a MOSFET

I have a power bank that I have remove the push button to turn on and off. The power bank turns on when I short both leads from the button and off when I short them again.

I measure the voltage across both leads from the button and it measures +3.5v when off and -2.7v when on. The polarity reverses, I put a 10k resistor across to sort of make a short and it works. Basically it don't need heave duty stuff. Note: It is a push button, not a switch.

Can I use an external MOSFET that it will be controlled by and external Arduino and if so, how can I hook it up?
I was thinking in sending a pulse to a relay to short the button leads, but I'd like something more reliable like a MOSFET or other neat things I might not know.

Keep it simple folks, and Thanks!

How is this proposed Arduino going to be powered? If it's powered from the same battery bank then you have to know if it's switching the high or the low voltage side of the battery.

MorganS:
How is this proposed Arduino going to be powered? If it's powered from the same battery bank then you have to know if it's switching the high or the low voltage side of the battery.

This arduino will be powered externally, anyways I could share a commune ground. I just need something to short the dam things that change polarity xD

Simple then. Make the common ground the most-negative of the two button wires and put a N-channel MOSFET in to switch the other wire to 'ground'.

Or use an opttocoupler, which frees you from the whole common-ground thing anyway.