It seems to me you mean chainset or crankset when you said chainwheel, if so it depends on the make AND model of the new and the old.
If the bcd of your chainset is such that you are able to replace your 39T small ring by a 34T, then you do not need a new bb.
In either case if I were you I would check to see whether the rear mech has the requisite wrap range to cover the extra tooth differences front and back.
I need to change the rear mech as well, that bits sorted. Just didn't want to buy the new chainset strip off the old one and then find it didn't fit and have to wait around until a new BB turned up. the existing chainset is Shimano A050 and the new one would be Shimano 2350.
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