Is there any way I can work on my Greek Golden Visa?

You will hire a Greek person to be the legal representative of the company.

The Golden Visa doesn't give you the right to get employment, but once you buy a hotel, there are other legal ways to get this permit as well.

Beneficiaries of the right to enter and obtain a permanent resident permit under the article 16 of Greek Immigration Law 4251/2014 are the non-EU/EEA citizens who intend to invest in Greece (investors), either personally or through a legal entity, provided that their investment project meets the conditions set by the legal framework, as outlined here. First, there are no restrictions regarding the sector of activity or the location of the investment project. The requirement that must be met by the investment is to have positive impact on national development and the economy. Investment activity may be implemented through the construction of new facilities (green field investments) or business acquisitions, restructuring or expansion of current activities (brown field investments). Factors taken into account for assessing the impact on national development and the economy are job creation, promotion of domestic resources and vertical integration of domestic production, export orientation, innovation and adoption of new technology. Second, the legal framework does not set specific limits regarding the total cost of the investment project. However an investor applying for a resident permit under this program should contribute to the investment with an amount of at least 250,000 euros, available through his or her own funds. The holders of such a resident permit for investment activity have access to the exercise of investment activity (as a legal representative, president, board member or chief executive officer). So you can exercise the business activity of your hotel under the above roles.