Interior or exterior could make a big difference. An exterior would actually worry me more - unless you had a good scaffold setup. Interior (assuming it's accessible) seems safer.
Plus - how solid is the mortar? I just took out an old and unused 35 foot 60"x18" plaster-covered brick chimney. But I hired a local general construction crew to take it down below roof and close in / shingle the hole - and we also had full access to the full length - attic to basement - as we renovate the house.
SWMBO and I proceeded to hand-disassemble the chimney a brick at a time right down to the footer. Actually very easy but very dirty work - the mortar was completely shot - more dust than bond. However, in the occasional spot where we hit an old repair where the mortar was still solid (or the plaster had been repaired with patching cement!) - the pace definitely slowed down. Nothing fancy - cold chisels, mallets, and pry bars at that point. Use goggles and good dust masks and have at it.
If you don't have that kind of all-sides, all-floors access - there is probably some way to collapse the chimney into itself a little at a time - and withdraw the bricks from the top - but that is going to be slow slogging.
(Tractor content - the loader made quick work of hauling the bricks out to the barn. At least I got some seat time out of the project!)