I didn't have a swing napper but I did carry Isabella on the Babybjorn for all her naps until she was 9 wo. Honestly, its quiet normal for her to want the swing, after all she is used to being rocked to sleep for 9 months. I also wouldn't worry about it so much at 5 weeks but you will need to eventually start making the transition to cot. Don't despair if shh/pat doesn't work straight away, it can take some time before your lo learns to self-soothe. Once the sitter takes over (& if you are still working on shh/pat), let her know this is the method you want used as sleep training.
Good luck
Layla