If original wire wheels, they are tubeless, 13", and I think the rim width is 4". Definitely measure them. The original tires for a series IV were either 6.00 x 13 or 5.90 x 13. You’ll find limited options to fit a 13" rim and match the original tire diameter. Original diameter appears to have been around 23.3" to 23.7".

A good SAOCA thread on the topic: http://www.sunbeamalpine.org/forum/showthread.php?t=24980