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Accepted Answer
Changing A record to point to Droplet IP is absolutely enough to make it work perfectly.
Changing Nameservers to DigitalOcean is only required if you want to use DigitalOcean Domain management (DigitalOcean Control Panel -> Networking). If you don’t want it, be free to keep your current settings. But that means, any change you want to make to domain will have be to done from your Domain register’s control panel.