I'd suggest the train as well.

Although both coach arrival and train to Gatwick departure stations have the same name, "Victoria", they are actually a substantial distance apart, and as your passenger has mobility issues, you may want to get a taxi anyway.

The main coach station is used for all departures, but the arrivals are split between the main station and the extension across Elizabeth Street. This would work fine if you knew when the bus was actually coming in but the long-distance ones can easily turn up anything from an hour early to an hour late compared to the notional arrival time, dependent on traffic.

Meanwhile, at the railway station, you do have the exact arrival time and platform shown. I would use the train, and a cab from Euston to Victoria.