External switch with Pico Lipo Shim?

I want to put a Pico-based project in a case and use a case-mounted switch with the LiPo SHIM for Pico. It looks like a momentary switch soldered to the connectors of the existing switch might work.

Has anyone tried this? Is there a better way to do that? A variant of the shim without the switch but with connectors for an external switch would be ideal.

The schematic is here if that helps, that switch is way down at the bottom.
Near as I can tell its a momentary none latching button. And not wired out to the edge connectors.
ppico_lipo.sch (shopify.com)