He could go to the London Underground ticket hall at King's Cross St Pancras to get his railcard added to his Oyster. Then it would be £2.05 to get to Whitechapel, and £1.65 to West Croydon.
Without a railcard, this would be £3.10 and £2.50 respectively on Oyster or contactless. I don't think any paper tickets would result in a saving despite the ability to use a railcard. (A paper single from St Pancras to Croydon Stations routed 'Not Underground' is £5.65 and even if it is valid via Whitechapel which I'm not sure about, Elizabeth Line barrier staff are likely to cause difficulty).