If my opponent reacts to Siphoning Strike using a spell like Hidden Blade to kill their own creature in response, does Siphoning Strike still channel 1 rune or would the premature death disrupt the timing?

No — Siphoning Strike will not channel a rune and will resolve with no effect.

Here's why. When your opponent responds with Hidden Blade and kills the unit, Hidden Blade resolves first. By the time Siphoning Strike resolves, its target is no longer at a battlefield (it's in the trash), making it illegal (Rule 359.3.e.2). The damage instruction is ignored.

Siphoning Strike's delayed trigger — "When it dies this turn, channel 1 rune exhausted" — is a linked instruction that references the targeted unit (Rule 359.3.e.14). Since the earlier instruction (dealing damage) is ignored because the target is illegal, the later linked instruction is also ignored (Rule 359.3.e.14.a). The delayed trigger is never created, so no rune is channeled regardless of whether the unit dies.