Yes. The law requires a director on record — not that the director own shares.
Uzbek law requires every LLC to have a director on record and does not require that person to hold shares — the director article expressly allows electing someone from outside the shareholders, and even handing management to an organisation under contract. A director provided under a services arrangement is therefore an ordinary application of the rule, not an exception to it — and it works in the open: the registry shows the director, the ownership records show the shareholders, and the bank identifies the director in person knowing the role is provided. (LLC Law, Art. 42 — lex.uz ↗)
Management on your written instruction — ownership, profit and control stay yours.
Part of the answer bank — 195 questions, each cited to the article it rests on.