No, he has basically entirely skirmisher elements.
Divers and Skirmishers are very similar classes but there are two major points of differentiation - their mobility and their defenses.
Divers have powerful, cooldown gated mobility spells that either have huge reach (Vi Q, Irelia Q, Camille E) or insane reliability (Pantheon W, Xin Zhao E). These spells are designed to get Divers onto the enemy backline. Skirmishers on the other hand don't have mobility spells on basic abilities with such raw gapclosing power. They instead have mobility that is much more persistent and repeatable - mostly very low cooldown, short range dashes (Fiora Q, Yasuo E), with the noticable exception being Gangplank, who simply just gets lots of speedboosts. Kled's E falls directly in the latter category, being a very short range dash with an effective 3 second cooldown lategame (2 casts on a 6 second cooldown).
For defensive tools, Divers often have very simple, relatively low-power tools, if any at all. Skirmishers on the other hand have incredibly powerful defensive tools, but they are much more gated (Wind Wall 26 second cooldown), they are often expressions of skill (Grand Challenge), and they often scale with offensive stats or reward offensive play (Valor). Kled's remount is a perfect example of this - its an insanely powerful defensive tool, but its only going to ever happen once in a long while and Kled has to play risky to get it.
While those two are really the only important things when it comes to classifying him as a Skirmisher over a Diver, the rest of his kit also leans into a Skirmisher playstyle. All his skills have massive bonus AD ratios. The ways his W works prevents him from saving his damage for a priority target like a Diver would want to. His ult grants him a massive AD scaling shield.
His ultimate isn't intimately tied to being a Skirmisher, but ultimates don't define what class a champion belongs to, unless its on a basic ability cooldown like Kassadin or Corki. Ultimates give champions access to tools from outside their class and give them a reason to be picked over similar champions. Kled's ult gives him the unique distinction of being a Skirmisher with hard engage.