It won't be as bad as you are imagining ResetPassword. Especially if you have a dummy to give to make things calmer and with less crying.
Side off the cot means you can cuddle right in, cuddle up to him but crucially, he will go to sleep in the cot, where he will sleep.
Is this likely to reduce the frequency of night wakings?
You need some realistic expectations. It might make a significant difference straight away. A baby getting plenty of daytime sleep, not over tired and so goes into a deep sleep easily should wake less frequently.
A baby who can find and manipulate their dummy in the dark to put it in themself may wake, but go back to sleep themself. A baby who can't do this may wake, but need a parent for a quick dummy plug to get back to sleep (which can be done in a semi conscious state from a sidecar cot)
A baby who is not getting enough sleep (or calories) over 24 hours is likely to be a light sleeper. Light sleepers wake frequently anyway and the more over tired baby is, the more help they need to settle.
In any rate, the main benefit of the sidecar cot and in-cot settling is being able to settle baby without having to move from under your duvet. So realistic expectations needed, in-cot settling is not always a magic wand. But it definately helps and is a step in the right direction.
Should I use this method for all sleep including naps or work on night sleep first then naps?
I did it at bedtime first. It depends how well baby takes to it. If, like susannaR, it's not difficult to establish then you might just need a few days to establish it for both naps and bedtime.
If it's trickier to establish, the concern would be baby getting over tired (so even harder to settle) if daytime naps reduce.