Picking the right transistor to replace a push-button?

I have a push-button on a on a surround-sound input changer, the one button shuffles through the four inputs. I want to replace this push button with Arduino control so I can use an IR remote to prevent going under my TV and press the button to switch between cable box, bu-ray-player & Roku. I have opened the device up and used a multi-meter to measure the push-button. I don' know how to pick a transistor with the information I measured. The leads of the button carry 3.3 volts and 0.1 micro-amps. I am using a Arduino Micro, which has 5 volt logic. It is a given I want a NPN transistor so the circuit isn't held complete if my Arduino gets unplugged. And I also know to ground them both together.
Do I need additional information?
How do I use this information to pick a transistor?
Do I need a resistor for the base to turn down the 5 volt logic?

An opto isolator might be one way - the output transistor will have no problem with
3.3V - and should have leakage a lot lower than 100nA (worth checking the datasheet for that).

With an isolator no need to worry about grounding.

Use any general purpose transistor like a 2N3904 with a 10K to 100K series resistor in the base of the transistor, this will give 2mA to 0.2mA base drive (approx) that will be overkill for the current you want but will not do any damage and will reduce noise intolerance. The transistor should fully switch off with the Arduino low level output voltage but if it doesn't then put another resistor the same value as the base resistor between base and emitter(ground).
Providing you don't go over 125 degrees ambient then the off the collector current (Icbo should be less than 100nA).
Or as Brattain Member said, use an opto-Isolator.