Simple answer: don't stick your fingers in it!
The power supply is more important: a small switched-mode supply with no earth connection has a 2.2nF Class-Y capacitor between the rectified mains and the 0V output. This means that the output will float at about 115V above ground, at high impedance. If you touch the reset pin, it gets a -115V pulse - so of course it's going to reset!
If you have an earthed power supply, it won't be a problem, you can touch it as much as you like, you would need to connect it to 0V with a piece of wire to make it reset.
With no track to the reset pin, I have never found a pull-up to be necessary, because there is no way to get a negative-going pulse to the pin.
The internal pull-up is somewhere between 22k and 85k.