Dead bird in my garden

Hi there
This is my first post and I hope it's ok to ask this here.
I'm after advice re a long tailed tit visiting my fat feeder. I've noticed the group flying about in surrounding trees over the summer and autumn but a few days ago we had what appeared to be a lone LTT visiting our fat feeder. It didn't appear to show any signs of being I'll- it wasn't slow/ lethargic, not puffed up, not showing food around its beak and not visiting the bird bath for a drink, but was definitely on it's own which I believe is not usual. Today I found a dead LTT nearby to the feeder. I am assuming it's the same one. We have had a cat hanging around the garden recently but I haven't seen it over the past couple of days. I'm wondering what to do? Do I assume it's just nature and the bird died of natural causes? Do I assume it the cat? Or do I play safe and take down my feeders just in case it was diseased? I was my feeders every 2weeks and only washed them at the weekend. Thanks for reading.