The later ones like this had 9mm gauge plastic wheelsets, normally moulded in silver. As CJI. says, the wheels are held in place by small tabs that would have been pressed down in the factory. Chances are they will break off when you attempt to lift them to put new wheels in. A small sliver of thin metal glued under the axleboxes will stop new wheels dropping out, but you'd need to be sparing with the glue. I'd recommend epoxy resin.
Incidentally Lone Star did actually do a Baby Deltic in their electric range, but it wasn't re-released in the later Treble-O-trains pushalong range, though the Derby Type 2 (Class 24) was.