There is a £17.60 anytime day single for Staplehurst-Woolwich Arsenal "via not London", but I can only seem to get the journey planners to offer a Staplehurst-Paddock Wood-Sevenoaks-Lewisham-Blackheath-Charlton-Woolwich route for that ticket (use the "Avoid" option in a journey planner and put in "London", or select "London (all)", as the station to be avoided). This may be related to the fact that Paddock Wood-Woolwich (via Strood only) is £17.70 for an anytime day single, whereas Paddock Wood-Woolwich (via Sevenoaks only) is only £15.20 for an anytime day single (or £14.40 for an offpeak day single.)
Otherwise, you need to buy two tickets: either Staplehurst-Paddock Wood, and Paddock Wood-Woolwich Arsenal (via Strood only): £4.50 + £17.70; or Staplehurst-Strood, and Strood-Woolwich: £12.10 + £10.70. (I have given prices for anytime day singles: for some of the tickets there is an offpeak day single for 10p less. And I have assumed that you will use Oyster PAYG between Woolwich and London City Airport.)