I am however a lazy person and it does indeed appear possible to do it without such a mission.
Indicators are held by 2 bolts (one on either side), 7mm diameter through the back of the indicator housing. You can use a small ratchet (the smallest one in a Halfords pro-kit is perfect) with a 7mm socket and there's just enough room to manoeuvre sticking your hands up there.
It's a little fiddly and all based on feel and guestimating where to put the ratchet until you get it right but it's certainly do-able. A replaced from left indicator is evidence of this.
So, before you start removing bumpers, give it a go.
