The problem with regarding them as cavalry is that there is not explicit reference to my knowledge of them serving to that capacity. Sparta was notoriously incapable when it came to fielding an effectual cavalry force, and although Agesilaus II did at one point succeed on that front, it was only temporary. At the moment, there are cavalry represented by Perioikoi, but even that seems to be a major stretch. To be able to employ horsemen in in warfare, one usually was landed nobility, and it is highly unlikely that vassals were able to do so. This can be supported by the fact that most of Sparta's cavalry came from league members rather than Laconia proper. If Skiritae were cavalry, we would expect historians like Xenophon, an experienced cavalry commander, to have mentioned it. Simply speaking, if there were Skiritae that were cavalry, it would be a small contingent representing some aristocratic caste since not all people could afford to use horses that way; the historians refer to Skiritae collectively as scouts, not a mere fraction.
On that front, Skiritae infantry armed to fight on the frontlines and used for recon are not an exception. The Silver Shields seem to have served a similar function in Alexander's campaigns.