Did they even have a say in the matter? And if so, was becoming an independent nation a possibility?
They weren't given a choice. Hong Kong had a long history of capitalism under British rule, but not a long history of republicanism. Hong Kong's first Legislative Council election was in 1985, one year after the Sino-British Joint Declaration that agreed on a 1997 handover. Democratization in Hong Kong only started in earnest after the handover was made inevitable.
That said, a small number of Hong Kongers did have a voice in the Sino-British negotiations. They were initially skeptical, then changed sides inexplicably mid way through the process. While there was no democracy under the majority of British rule, some extremely rich Chinese did have influence in the decisions of the colonial governor. In 1982, the most influential Chinese was Chung Sze-yuen, heir to a manufacturing business and the chairman of the Federation of Hong Kong Industries. When China pushed for the handover of Hong Kong, Chung initially pressed the Thatcher government to resist. In 1984, Chung and fellow tycoon Lee Quo-wei traveled to Beijing to meet Deng Xiaoping. When they returned, they suddenly became the mainland's most active partisans and started building a coalition of fellow tycoons to support the mainland's vision for Hong Kong. They also didn't return alone, but with a handler: Xu Jiatun, head of Xinhua news. When Chung made a very minor criticism of the handover, claiming it would lead to brain drain, Xinhua ran several articles against him, and he ceased being critical of China for the remainder of the handover process.
Why did the only Hong Kongers who had a say in the handover - the tycoons - suddenly flip? There are obviously no reliable accounts of the meeting of Deng, Chung, and Lee, but the lockstep actions of the CCP and Hong Kong's rich list in the following years indicate that the two found common cause in suppressing democracy. Hong Kong's tycoons benefited from the colonial government's mismanagement of Hong Kong's land and economy. British Hong Kong lacked any strong competition law, and maintained extremely restrictive zoning laws that confined residential development to a small portion of the island, benefiting existing landlords. Any democratic government in Hong Kong would have reformed both these inefficiencies.
The way the tycoons chose to "moderate" democracy was by working with the mainland to rig the constitutional drafting process. In 1985, Deng Xiaoping pressured the British to allow the mainland National People's Congress to convene a Basic Law Drafting Committee for Hong Kong, which was effectively led by none other than Xu Jiatun. The committee had 36 mainlanders and only 23 Hong Kongers, but was supplemented with a Basic Law Consultative Committee that was only made up of Hong Kongers. However, a majority of the BLCC were also business magnates and members of Chung's Federation of Industry, so this body was hardly objective.
The BLCC was revealed as a fraud by its first meeting, when tycoon Pao Yue-kong (a member of the Drafting Committee but not the Consultative Committee) walked in and read a list of 19 members the BLCC "will elect" to its executive committee, as the government does in the mainland. This triggered a wave of press outrage and forced a re-vote, but the same 19 members were still elected. Vincent Lo, who organized the "re-vote" fraud as a way of killing the press story, organized the "Group of 89" after the incident to push the tycoon's vision of a corporate democracy, while the members not affiliated with big business formed the smaller "Group of 190" (their name had nothing to do with the size of their bloc).
The shape of corporate democracy would be revealed by the "Cha Proposal", drafted by famous author and media mogul Louis Cha/Jin Yong. Under the proposal, half of the seats in Hong Kong's Legislative Council would be elected by professional and business associations called "functional constituencies". This amounted to almost half of Hong Kong's legislature being directly appointed by the island's corporations, with a four exceptions in the Functional Constituencies for educators, healthcare workers, social welfare, and labor. Lo rallied his bloc to pass the proposal, and it forms the basis of Hong Kong's voting system to this day. The system has led to some absurd results: for example, the second party in the 1998 election won 10 seats with 3.4% of the vote, while the first party won 13 seats with almost 43% of the vote.
The second major reason Hong Kong's business class supported reunification was that they had greatly bolstered their fortunes after Deng Xiaoping's reforms. Until those reforms, Hong Kong's GDP growth was relatively slow compared to other capitalist East Asian territories. The island had a greater GDP per capita than Japan in 1950, but, by 1975, Japan's GDP per capita was twice that of Hong Kong. Hong Kong's GDP skyrocketed after China's transition to capitalism, and by 1992 - the year Japan's boom ended - Japan's GDP per capita was only 15% higher than Hong Kong's. Hong Kong became a conduit for international investment into China and a go-between for Chinese state owned enterprise and the rest of the world. This new wealth, however, was not distributed evenly, and, from 1976 to 1996, Hong Kong's Gini coefficient had risen from a normal 0.43 to 0.518 - the highest level of income inequality in the developed world. Hong Kong's business class benefited from their privileged position between international investors and the mainland, and also took immense loans from Chinese state banks.
In short, most Hong Kongers had no say in the British colonial administration until after the British had already written them off. Those that did initially opposed the handover, but quickly changed sides when they realized that Beijing would place the island under their control and allow them to maintain the colonial-era policies that enriched them.
Sources:
Poon, Alice. Land and the Ruling Class in Hong Kong. <This isn't really an academic history book, but more of a primary source. Written by the aide to one of Hong Kong's biggest real estate tycoons, it provides an inside account of how the tycoons benefited from the British land law, which is still in force today>
Ash, Robert. ‘Like Fish Finding Water’: Economic Relations between Hong Kong and China.
Maddison, Angus. Maddison Project Historical GDP.
Ghai, Yash. Hong Kong's New Constitutional Order: The Resumption of Chinese Sovereignty and the Basic Law.
Poon, Kit. The Impasse Over Constitutional Reform: Negotiating Democracy in Hong Kong.
Lee, Kim et, al. Financialization and Economic Inequality in Hong Kong: The Cost of the Finance-led Growth Regime.
Hung, Cheuk. Income Inequality in Hong Kong and Singapore.
Pepper, Suzanne. Keeping Democracy at Bay: Hong Kong and the Challenge of Chinese Political Reform.