Is the cot next to your bed? That would be the best place to start, if it's not. Then if you make sure dummy is very easy to find (which it needs to be for baby to find when older), you should be able to do dummy reinserts without even opening your eyes, just lean an arm into the cot.
Frequent waking is not because of the dummy. A dummy helps baby go to sleep. The process of going go sleep usually usually only takes 5 or 10 minutes. Once asleep the muscles of the mouth/jaw relax and the dummy drops. It's meant to.
If baby is not getting into a deep sleep and staying asleep - that's a completely seperate issue. All the dummy does is help baby go to sleep when they wake. If you ditch the dummy (as well as that being a SIDS risk) all you have is a baby waking frequently and also hard to get back to sleep.
So this waking frequently. Fretful nights are most often due to:
● Over Tired
A baby getting lots of sleep is easier to get to sleep, gets into a deep sleep easily, links sleep cycles without waking and so wakes less frequently.
A baby not getting enough sleep over an extended period (24/48 hours) will find it more difficult to get to sleep. Once asleep will find it difficult to get to the deep sleep phase so will stay light sleeping for more time. Then more likely to be disturbed when moving through sleep cycles or due to external factors. So the over tiredness cycles and baby's sleep gets more and more fractured and broken.
The way to deal with this is to focus on daytime naps. Make them more frequent, less awake time.
● Low Level Hunger
This doesn't mean the sort of hunger you get just before a feed. It means a baby whos calorie intake is on the low side overall. So baby has much fewer reserves available to help them sleep longer stretches at night.
The way to deal with this is also to focus on the daytime. Calorie load in the daytime with more frequent feeds. Bigger feeds isn't usually the way because if of the limitations of stomach size. But having more bottles per day, closer together, increases calorie intake.
Also watch out for the early weaning trap. Early weaning foods are low calorie. As such should not replace milk, otherwise total calorie intake drops. Milk feeds need maintaining, possibly even increasing, during early weaning. Solids should be on top of milk, not instead of.
● Place Of Falling Asleep
It's important that baby stays asleep where they fall asleep. So don't move baby once asleep, if possible.