how did non skirmishing bow armed cavalry fight?

[eques]

Ghulams, bucelarii, achaemenids, Sassanids etc?

Did they loose off a volley before charging in? Were some bow and some not? Did they switch between the skirmishing and shock role as needed?

[aligern]

Maurice's Strategikon is a good guide. The Byzantine cavalry advance shooting overhead, with lancers in the front ranks. It looks like Persians stand and shoot, or afvance shooting.
Steppe peopkes would appear to have large numbers of close order cavalry who stand and shoot , evading if necessary . They detach units to skirmish , which return to the main battle line when they have completed a round of shooting. The main line is capable of stopping a charge by bowshots alone.

[Patrick Waterson]

This should give some sort of idea:

"Among the Sarmatæ the general's voice was not alone to be heard. They encouraged one another not to begin the battle with volleys of arrows; they must, they said, anticipate attack by a hand to hand charge. Then followed every variety of conflict. The Parthians, accustomed to pursue or fly with equal science, deployed their squadrons, and sought scope for their missiles. The Sarmatæ, throwing aside their bows, which at a shorter range are effective, rushed on with pikes [contis = lances] and swords. Sometimes, as in a cavalry-action, there would be alternate advances and retreats, then, again, close fighting, in which, breast to breast, with the clash of arms, they repulsed the foe or were themselves repulsed. And now the Albanians and Iberians seized, and hurled the Parthians from their steeds, and embarrassed their enemy with a double attack, pressed as they were by the cavalry on the heights [super eques = the higher cavalry] and by the nearer [proprioribus = closer] blows of the infantry. Meanwhile Pharasmanes and Orodes, who, as they cheered on the brave and supported the wavering, were conspicuous to all, and so recognised each other, rushed to the combat with a shout, with javelins [telis = missiles], and galloping chargers, Pharasmanes with the greater impetuosity, for he pierced his enemy's helmet at a stroke. But he could not repeat the blow, as he was hurried onwards by his horse, and the wounded man was protected by the bravest of his guards. A rumour that he was slain, which was believed by mistake, struck panic into the Parthians, and they yielded the victory." - Tacitus, Annals VI.35

The Parthians seem to prefer a skirmish, at least to open the action.  The Sarmatians are keen to close immediately, perhaps because Parthian bows outrange theirs, and what follows is a mixed action in formations sufficiently loose for leaders to see each other and move into individual combat, but sufficiently close or intermingled for 'breast to breast' fighting to occur.

[Duncan Head]

Did they loose off a volley before charging in? Were some bow and some not? Did they switch between the skirmishing and shock role as needed?

All of the above and none, I think.

In the first cavalry exercise forty-six infantry and one hundred seventy-four cavalry soldiers made up one section. At the sound of the drum the infantry fired three volleys of arrows and then "opened the gate" for the cavalry to charge out. The cavalry fired three times to the front, turned, and fired twice to their rear... In the second cavalry exercise one hundred and seventy-four men were divided into three sections. Each section was separated into four lines. When the drum sounded the first section came out, each line firing four volleys of arrows. They stopped and the front two lines fixed their spears. The front two lines uttered a loud cry and made three stabs. The rear two lines also made a loud cry. The entire section turned their horses and fired twice to the rear before returning to their old places.