I have a Zone 2-4 monthly on Oyster with £xx pre-pay.

I need to make a journey from Woodside Park (Z4) to Canary Wharf.

I intend to go via Bank and then change on to the DLR. Do I need to
swipe at the DLR entrance ?

Not really, buy you definitely need to touch-in at Woodside Park as you
will begin to use PAYG after Camden Town.

I thought that by swiping out at Canary Wharf, the correct fare would be
deducted.

It will as long as you touched-in at Woodside Park.

But if my Oyster is checked on the DLR train, what will it show ?

Any ideas ?

It will show that you touched-in at Woodside Park.