Can you use Zed legend ability to draw 1 even if you have no cards to discard?

Yes. Master of Shadows (Zed's legend) says "Disempower me, [T]: Discard 1, then draw 1." The discard is part of the effect, not a cost — the costs are only disempowering and exhausting. So with an empty hand you discard 0 and still draw 1 (Rule 422.4: discard as many as possible, then continue with the rest of the effect).

This is the opposite of the Deceiver (LeBlanc) legend, whose "discard 1" sits before "to" as a cost — that one can't be activated with an empty hand (Rule 422.3). For Zed, the "then" wording makes the draw unconditional.