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Has any one tried to use offshore companies to trade on binance, bybit?

Depends whether you are resident. In your case most likely 0%.

https://taxsummaries.pwc.com/barbados/corporate/taxes-on-corporate-income said:
Companies resident in Barbados are taxed on income earned from all sources, whether generated within or outside of Barbados, less expenses incurred for the purpose of producing assessable income in a fiscal period not to exceed 53 weeks. Non-resident companies are generally only taxed on income derived from sources and operations conducted within Barbados.
 
Depends whether you are resident. In your case most likely 0%.
Okey, cool. So I just need to manage it from another country outside of Barbados. How it that proven? By me having a registered address in another country or? But probably Barbados tax authorities have never challenged this?

Also, is it possible that the company trades the crypto and acts like a holding company while I hold the wallet and the private keys in my hand in another country?