The main question is what diameter the axles are. If they are standard 10mm axles you will almost certainly be able to swap just the axles for hollow quick release ones. That's doable at home and easy for a bike shop (you need a flat "cone spanner" and preferably a vice). The only parts you need are front and rear QR axles and skewers plus new grease. I'd probably change the bearings and cones when I had it apart, depending on their condition. But you don't have to.
From looking at this it seems to have fairly standard 20" wheels. From a mention in another search result I suspect it may have a 9mm diameter front axle which would make it tricky. It might be possible to fit a 10mm axle in there if you can find compatible cones - you need to either try it or find someone who has. But the rear wheel looks like a standard derailleur hub, so it should have a 10mm axle.
I suggest measuring the axle diameter as your first step. If they're both 10mm it'll be easy.