You will be entering the Schengen area at SPL so passport control is needed. If you have any worries ask KLM to provide assistance. The Schipol handling agents will meet you at the gate and take you through formalities to your departure gate. While you may be the last off the arriving aeroplane you could be first on the connecting flight. Don't worry, you won't get a wheelchair, it will be a golfcart.
You don't have to prove you need assistance, they must provide it. It's included in your ticket price, so there is no excuse for not asking. They do ask for 72 hours notice, so ask for it sooner rather than later. A phone call to the airline you booked with is needed, you can't do this on-line
I wouldn't do this at Gatwick, which employs pound scum for this, but think you should be OK in the Netherlands.