As for proving a benefit, there's 9 indexes on this table and if four never get used they're just dead weight objects.
I can't make that call for you.
Also I don't know replication so I don't know how & what consequences it could have.
Just a P.S. 4 unused indexes that are never written to and never read to are not THAT harmful.
Are they filtered? => maybe a wrong plan is ignoring them
Are they unique keys? => can't drop
What size are they taking? => 1mb, 1 tb? Anywhere in between?
When's the last time you had to maintain them?
Are you really that short on HD space that you need to worry about 10 MB <insert your real figures> of indexes.
Why are you focussing on that table rather than the script on the whole DB and finding the biggest possible dead weight that has to most space used & writes without reads?