In Support of The Dummy
I absolutely would not give up the dummy at this point. As well as it not being (NHS and Lullaby Trust) recommended to give up a dummy before 6 months, or use it inconsistently - it will also create much more crying in the process of getting to sleep.
Stopping dummy use will not stop frequent wake ups
Frequent wake ups are to do with (a) baby being overtired (b) baby not going to sleep where they stay asleep, for example falling asleep in your arms (c) developmental and will be grown out of in time
The dummy is for going to sleep, not staying asleep
The purpose of the dummy ends once baby is asleep. It is there to help baby to relax their body and independently sooth to sleep. Once asleep then all muscles will slacken, including jaw muscles and dummy drops.
Good use of dummy means it's in the mouth for about 10 mins, from baby being awake until fully asleep.
Linking sleep cycles
Assuming you have in place that baby goes to sleep from fully awake in the cot, linking sleep cycles is developmental but is made infinitely more difficult for baby to do if overtired.
If baby is not getting enough sleep over a 24/48 hour period, then all sleep is likely to be lighter and more fretful. This means that instead of being able to go from deep sleep to a brief period of light sleep and back to deep sleep without waking up, baby is more likely to spend substantial periods of time in light sleep and so between cycles there are awake times, rather than light sleep.
This is not dummy related.
Assuming baby is not over tired, is having ample sleep over a 24/48 hour period and also has good sleep hygiene, then it's just a matter of baby making the developmental leap to link cycles. Like all development stages, it varies between individuals.
Reinserting own dummy
In time, baby can learn to find and replace their own dummy. This happens generally around 7-9 months old (ish). There are things you can do during the daytime to improve fine motor skills and pincer grip to help this.
But in fact, as mentioned above, is baby isn't over tired and has good sleep hygiene then the mid-cycle wakes reduce anyway, so dummy re-inserts become less necessary anyway.
Without a dummy, you're likely to have far more sleep issues by 9 months old and you'll be wishing use kept going with the dummy because sleep would have been resolved.
In summary
Dummies are ACE
They are so simple and effective. There is no easier and quicker way to get baby to sleep without crying. Any other sleep training method will involve a lot of crying. I always favour the gentle, no crying and no distress methods and the dummy is THE BEST way to achieve this. I wouldn't want a sub-12 month old screaming to sleep, certainly not a sub-6 month old.
The dummy is there to make going to sleep easier.
Without it, if you don't like listening to your baby cry, you're likely to end up either cosleeping or rocking to sleep. Nothing wrong with co-sleeping or rocking to sleep, but these are not independent sleep. Dummy helps achieve independent sleep, without any crying.
If you can tolerate some crying then you can achieve getting baby to sleep independently, in the cot from fully awake to fully asleep. But it will take a lot longer than a dummy resettle, and with a lot more crying.
Whichever alternate settling method you choose, if you don't solve the original overtired or developmental issues then it won't solve the frequent waking issue. Just makes life harder.
As you may be able to tell, I am a HUGE fan of the dummy.