I would not recommend doing either Oyster or contactless. The problem is that you have to adhere to maximum journey times between touch in and touch out, and also keep track of out-of-station-interchanges joining journeys together. If this happens then you’ll be charged two maximum fares and neither will count towards the daily cap.
There is one potential compromise which is to buy a weekly zone 1-9 travelcard on your Oyster card and then cancel the Oyster card at the end of the day. This will result in the unused part of the travelcard being refunded. It will also result in the Oyster card being cancelled. A replacement will now cost £7 and is not refundable.
Good luck with the challenge though.