Ah, playing around with it I see that starting from inside the Oyster zone is considerably cheaper.
Avoiding the tube you could always do Willesden Junction to Clapham Junction on London Overground (it's a train) and then to Carshalton from there, may take a bit longer though.
Hmm, no trains from Willesden to Clapham Junction this weekend, you'd have to go Willesden to Richmond and then change to get to CLJ (at least the Richmond to Clapham trains are fast).
Getting to Willesden you could cycle (16 miles) or train from Gerrard's Cross to Wembley Stadium (£15.10!) and then cycle the 3 miles to Willesden Junction.
Using the Oyster single fare finder:
https://tfl.gov.uk/fares-and-payments/fares/single-fare-finder?intcmp=1660Willesden Junction to Carshalton is only £2.60 with Oyster (off peak) if you avoid Zone 1 (which you would going via Clapham Junction).
But if you're going to cycle 16 miles then I wouldn't head to Willesden, I'd probably head South to somewhere like Whitton (still 16 miles) and then Oyster the train to Clapham Junction and then Carshalton.
Alternatively cycling all the way in and then London Victoria to Carshalton on the train is £3.30 with Oyster (off peak) and far less faff.
The two times I've done the SA400 I wasn't interested in riding any further and so I got the train from Gerrard's Cross to Marylebone, cycled down to Paddington and plonked the bike on the tube all the way back to East Putney. I wasn't that worried about the cost of the train ticket at that point.
This is the other map that may be useful:
http://content.tfl.gov.uk/bicycles-on-public-transport.pdf although it annoyingly doesn't have all of the trains on it, so you have to try and combine that with the one I linked to above but careful to avoid the deep tube lines where bikes are not allowed.
tl;dr from hereIf I didn't want to cycle all the way in to Victoria what I'd probably do is:-
ChStP to Chorleywood Rail station is ~4 miles cycle. Oyster from there to Carshalton "Avoiding Zone 1 via West Hampstead (or Kilburn/Brondesbury), Willesden Junction and Clapham Junction" is £3.10 (off peak).
So that's Metropolitan line (fine with a bike) from Chorleywood to Finchley Road, short cycle (or train/tube if lazy) to West Hampstead or Brondesbury, then train to Richmond (because Willesden to Shepherd's Bush is closed this weekend so you can't get to CLJ directly), quick train to Clapham Junction, then train to Carshalton.