I can never remember if it's swathing bands or swaddling bands (as the two are just about interchangeable) but 'swadling' to rhyme with 'cradling' is just plain silly. 
Technically, the probability is that a vowel followed by two consonants indicates a 'short' vowel sound. (And, 'a' after a 'w' is almost always said as 'o' as in 'orange') Note that MM removed a 'd' to help us understand the odd pronunciation more clearly. Start messing about with doubled consonants and English becomes even more difficult to learn to read and spell.
I feel very strongly about this as I taught phonics and studied in some depth.