haverina - technically co-sleeping refers to a mother/parents sharing a room with their baby regardless of cot/bed proximity. Bed sharing is what most people mean by co-sleeping (inc. me sorry!).
I had the girls in their cot next to the bed but would feed them to sleep and then transfer them to their cot if I was still awake when they went to sleep or if I woke before they did I would transfer then. I used a cot sheet for them to sleep on to make transferring easier (no 'cold sheet shock' to wake them up). They slept next to me so we went DH, me, baby, cot rather than DH, baby, me. The bed was set up so the baby wasn't covered by our bedding and they had their own sheet/blanket as ness.
Personally and not in any capacity as a BFPS/MS, I think that the dummy to sleep to prevent cot-death mechanism is a bit mis-understood. I don't think that a dummy prevents SIDS so much as the absence of a dummy when a baby usually has one might be a risk factor.
If a child didn't have a dummy on a specifc sleep it increased the chance, that statistically, they would have die from SIDS (this is if they normally had a dummy to go to sleep). Babies who died of SIDS who normally took a dummy to sleep were more likely to have not had a dummy on that last sleep.
I don't know if the researchers actually parsed the reasons behind the baby not having a dummy on that last sleep:-
if it was the parents forgot to give it to them/didn't have a dummy to give to them - if it was the case in all the deaths of babies who always had a dummy to sleep then dummy would be conferring a protective effect on the baby. It could be that the baby rousing slightly to replace the dummy during the night might be enough to stop baby going into too deep a sleep/the dummy was triggering breathing reflexes/other physiological mechanism that prevents SIDS,
if the baby was asleep/unusually sleepy before they would normally be put down for a nap the dummy might not being given to help them sleep - then you could infer that the baby was behaving out of their normal parameters as so was already displaying signs that something wasn't right [not that you would expect parents to wake a baby that has fallen asleep earlier than usual so I'm not casting blame on the parents],
if the baby refused to take a dummy or was unable to suckle on it so it was removed - in that case there was possibly a physiological problem/illness already in process that then refusing a dummy was just an indicator that something was beginning to go wrong not that the dummy refusal caused the death.
I think if you do give a dummy you need to give it every single time they go to sleep and if they refuse it or are unable to take the dummy on a particular occasion a closer eye should be kept on the baby just to be sure.
If you or the baby don't want to give/take a dummy in the first place then bfing before sleep and co-sleeping with in arms reach (either in a cot or next to mum in a safe bed space) or in during the day baby sleeping in the same area as the parents are would have a similar effect in keeping baby out of very deep sleep/triggering breathing reflexes/etc.
Sorry for essay 