How to get of rats and not endanger birds

Hello

Yesterday I spotted a large brown rat in our garden, out during the day. I saw it again today. I would like some advice on how to best trap the rat without putting our birds at risk. We have two squirrel proof feeders having from barckets on the wall but I am not sure if the rat is eating what is dropped by the birds.

I have a supercat rat trap, but I am afraid of injuring or killing birds with it. I love the birds - we have blue tits, great tits, long tailed tits, robins, dunnocks, blackbirds, greater spooted woodpeckers, stock doves, blackcaps, wood pidgeons visiting us daily and I want to keep them safe. Any advice on what to do?

Many thanks