I know that on CoinMarketCap you can find the total capitalization of a coin/token, but often this kind of data is not available because, maybe, the project is too little or, in the worst-case scenario, the project doesn't want this data to be visible (sometimes they use "self-declared" information about the market cap).
Got it and that's why the fully diluted marketcap can be manipulated.
Does exist a website/explorer that could directly provide this information?
The only thing that can be done to check it manually through etherscan but I'm sure that it will also a bit difficult to determine how much the circulating supply that available in the market as a site like etherscan or bscscan will be only mentioning the total supply.
Another solution I was thinking about was to calculate the market cap by myself using blockchain explorers like Bscscan, the idea is to check the circulating supply that the explorer detects and confront it with the price shown on CMC (even better if directly checked on Pancakeswap) and do the math.
It may no accurate remember that what I have said that above.
Could this be an acceptable solution to have, at least, an estimate of total capitalization?
It's not an acceptable solution. The only team who knows how much the real circulating supply in the market. It's quite difficult to know this since you will be found the data about total supply from bscscan.