Sorry to see you didn't get any replies yet.
Can I just do it for some naps, plus bedtime?
Yes. I found that my DS learned a certain way of sleeping, a certain habit, for each nap. I have also seen it on the forums. So pick a nap and shush/pat for that one, when you have one nap going down well you can move onto another.
FWIW I also think it's probably worth LO learning to sleep in the car or push chair as you have another young child and likely need to get out and about to toddler groups, the park etc.
It's really helpful if you can keep each day pretty much the same so for example always doing sleep training in the cot at home for nap 1 and always using push chair for nap 2 (even if it is indoors). Make sense? So you don't randomly try one or two naps per day without making it a consistent routine. Consistency is the key when you have LO forming sleep habits whatever you want them to be.
You can also try some W2S at the 45 min mark. It is supposed to begin 10 min before the short nap wake up and continue for 20 mins beyond the transition (so this can be 30 or more min) but you likely don't have that time, I would try even 5-10 mins, in the room at 40min into the nap and try for 10. To me it is worth a try, if LO wakes fully either spend time to resettle or get her in the sling to continue the nap.
Her adjusted age is 1 month but you seem to be getting UT naps and have mentioned UT - a 1 month old can have a guidance time of 1hr 15 min so perhaps you need to increase the A time too?
Also for LOs with adjusted again they can gradually catch up so you will need to observe her A times as the weeks and months go by and not always be stuck to her adjusted age for guidance, be open to her needing the younger or older A times - hope that makes sense.