Hard wiring to replace CR2032 battery

Hey all, I'm looking to do a small arduino project and was hoping for a little advice.

The project is to use an arduino nano to fake steps on a cheap pedometer.

My plan is to wire the weighted pendulum switch in the pedometer to the arduino and trigger a pulse every second to simulate a step and increase the count.
I would also like to remove the CR2032 battery and use the arduino to supply power so I don't have to worry about losing power on the pedometer.
I will be powering the arduino via usb (5V)

Looking for some advice as to how to do this.

Would it be safe to just wire the positive and negative battery terminals on the pedometer to the 3.3v and ground on the arduino? or is the extra 0.3v likely to damage the pedometer?
When sending the pulse to simulate the switch closing, I assume this would also need to be 3v, would I have to reduce whichever digital output I use from 5v to 3 for this? If so hows best to do this?

thanks in advance.

I doubt that 0.3 V extra will damage the pedometer. But 5V on an input certainly will. By the way, the jog switch probably grounds a high signal line, so you want to imitate a switch closure, not send a pulse.

Best to use a 3.3V Arduino for everything (like a $2 ebay Pro Mini).

Great thanks, I'll give it a try wiring the pedometer into 3.3v.

As for grounding the pin would I be right in thinking that using a transistor across the switch would work to close the circuit?

Ordered a 3.3v mini.

Thanks for the advice.

a transistor across the switch would work

Yes, use an NPN transistor (open collector) with 100K or even 1 Meg base resistor. Connect the grounds, of course.