Glad you've tried a dummy! Firstly, sleep wise I think everything is pretty normal for four weeks old (sorry!!) So please don't feel that your doing anything wrong here.
Ultimately as long as your baby is fed, whatever combination this is will be perfect for them. You need rest and expressing for night feeds or so you can get out of the house is a great idea and ultimately will lead to happier better rested parents. We used a dummy and if baby was still crying then fed him, however if he just needed to suck he would drift off. It also then in the longer run helped us recognise his hunger cues better. At 6 weeks you are definitely well established with BF and it should have no effect.
Tips:
Get a Hakka or similar to collect let down milk when feeding from the other breast, sometimes this can be a good 50mls and every little counts!
If pumping longer term an electric pump is amazing and normally can be rented, you will however feel like a milking cow 
You might have to try a few brands of bottle/dummy, just ensure dummies are othodontic.
If stuck you can use your little finger for baby to suck on if you think they aren't hungry and just want to suck to save your nips!
Main & most important one.........do whatever gets you through this very hard and new phase of your life, trust your instincts and never feel like you've let anyone down or done the wrong thing. You do what is needed at the time to keep you all fed, warm and healthy.
We had a very sucky baby and a dummy was a godsend, and you'll find that the majority of other parents bar those with babies who refuse dummies will say the same thing - everyone in baby groups when your new parents are thinking they are being judged by the others, just be brave and be the one who does what they need to do and others will soon follow your lead breathing a sigh of relief!!!
Good luck x