LTC4412 as a High Side Power Switch for Single-cell Li-ion battery

I'm planning to use LTC4412 as a user controllable MOSFET switch. I'll post a image of my schematic for better clarity.

The range of Vin will be from 2.85-4.35V and I've used an SPDT slide switch with a minimum contact current of 1uA. It will be used to turn on and off the IC through the CONTROL pin. I'm planning to use SI9433BDY-T1-E3 as the P-channel MOSFET. I've done the simulation on LT Spice and observed only around a 13mV drain-source drop. Would like to get a confirmation whether this MOSFET is the right choice?

Finally, I would like to attach an LED on the STAT pin in such a way that whenever the switch is closed, the LED should glow. If I use LTST-C193KRKT-5A, how much resistance would I have to pull-up/down the LED to?

Thanks in Advance