If your LO is not reliant on the dummy for sleep (ie you have been removing as you say you have) then I wouldn't worry about keeping it but neither would I worry about dropping it. Using it all the way to sleep means it becomes a prop and a baby reliant on it for sleep shouldn't have it dropped cold turkey (SIDS guidance).
PUPD is a method intended for older LOs and a method of last resort. I wouldn't advise it at this age. Shush/pat is the way to go.
What's different about the pram nap - is the pram on the move? Rocking?
Some people actually prefer LO to be able to sleep well in a pram so you could even consider all naps in there whether at home or out and about as it does free up your arms to be able to do other stuff.
Sleep training does take time, shush/pat and PUPD are not quick fixes or no-cry solutions, they are methods whereby your LO is supported by you whilst they learn to sleep independently.
My question is...if he only has 45 mins do I then keep him awake to his next nap time or as I am currently doing put him down after around 1hr30mins which usually ends up not long after his feed?
This is really your choice. In the books Tracy kept LOs up to the next timed nap which meant some super long A times, it can help to establish a good routine and independent sleeping much more quickly but can also be very hard work as LO is bound to get OT. Often on the forums people prefer to go slower which means timing the A from when LO wakes at a short nap and putting them down at the end of the A time rather than a 'set' nap time.