(Corrects number of H1N1 swine flu deaths confirmed by CDC in Mexico in paragraph 9 to seven from 84)

* Fewer Mexicans head to hospitals with flu

* Mexico outbreak may not be as severe as feared, US says

* Hong Kong hotel sealed off after flu case found

* WHO says "no doubt" vaccine possible (Adds France and Florida cases, call for end to pork curbs)

By Alistair Bell

MEXICO CITY, May 1 (Reuters) - Mexico voiced hope on Friday it might be getting control of an outbreak of a new flu strain that has killed up to 176 people there, shut down large parts of the country and raised fears of a global epidemic.

The U.S. Centers for Disease Control and Prevention said Mexico's outbreak of the new H1N1 swine flu virus may not be as severe as it looked at first, citing many mild cases that were not immediately noticed.

Worldwide, 14 countries have confirmed cases. Almost all infections outside Mexico have been mild, and only a handful of patients have required hospital treatment.