The top hats might be OK, but if it was me, I’d replace the lot. TF will be the best place to start.
Yup do that it’s not worth **** about putting it back together to find you still have some play!
As you have an industry standard 15mm eyelet shock. You could replace the tops hats with a solid dowel (3 piece hardware), top hats and ceramic bushing/s (harder wearing alternative of what you’ve got) or roller bearings if high rotation. All you need to know is the width (should be in your bikes spec) and the bolt size, most commonly 6 or 8mm.
Make sure the new eyelet bushing and hardware is properly centred and don’t forget to blue loctite the bolts (just the threads!) or they will keep working loose and damage the bolts, shock and/or your frame!