If he's never regularly napped in bed then it is only natural that it will take some time for him to be comfortable there and he is likely, at least short term, to need help to settle. At just 4 months I would start with shh pat - Shush-pat - How to
PUPD is quite stimulating and really only a last resort at this age. Shh pat is gentler on you both and easier to transition from arms to crib.
Has he had a routine before or has every day been different? If he's never had a particularly structured day then it would be worth spending two or three days just observing him and recording when he seems to show sleep cues, when he sleeps, how long for etc (like you have above) and then posting it here so we can help you with a routine to aim for. Roughly speaking a typical routine at this age on BW would be about 2h awake time with two 1.5-2h naps and a catnap.
There are some sample routine on the EASY FAQs and some useful links about getting started
. Let us know what you think and we can hopefully help you to get him napping more happily in bed x