You don't have to pass through immigration, but you will have to pass through security. The flight will be from the H-pier (minimum facility, for LCCs) so you'll wait in the main departures area until about 40 minutes before departure, then you can sharpen your elbows for the rush.
Your extra legroom seat will also get you priority boarding, which easyJet manage as a segregated queue. Do note the dimensions of your carry-ons (56 x 45 x 25cm for the 1st and 45 x 36 x 20cm for the 2nd) as it's quite expensive to gate-check luggage if they choose to enforce it strictly.
I like easyJet, but it (and Stansted arrivals) will feel like quite a culture shock after J on SQ!
2h is fairly tight, although Schiphol is a good airport for it to be tight in. IIRC, the SQ flight lands at one of the piers in Departures 3, which is near H, so that saves some of the longer walks in the airport. easyJet do have a 'flat tyre rule' if you miss your flight (albeit with a €36 fee).