Additional clarifying points.
1. You are already isolating your ’router’ from your "WiFi receiver" by using WiFi. This is a good thing.
In this scenario, a single LPS to your "WiFi receiver" is a good first step.
2. IF you choose to run ’wire,’ i.e. the LAN cable from your ’router’ to the "WiFi receiver"....
Then, powering your ’router’ with an LPS becomes more critical...for the reasons @almarg highlighted in his post.
Having a LPS that can power both is ideal and also allows you to test cable vs WiFi (to determine which one you prefer).
1. You are already isolating your ’router’ from your "WiFi receiver" by using WiFi. This is a good thing.
In this scenario, a single LPS to your "WiFi receiver" is a good first step.
2. IF you choose to run ’wire,’ i.e. the LAN cable from your ’router’ to the "WiFi receiver"....
Then, powering your ’router’ with an LPS becomes more critical...for the reasons @almarg highlighted in his post.
Having a LPS that can power both is ideal and also allows you to test cable vs WiFi (to determine which one you prefer).