For some reason I'd make the point to this director and raise another complaint against him about withholding the letter of employment and his attempt of blackmail... I'd bet the owner would love to hear about this too; and bullies will only stop when someone doesn't back down.
I'd also go around him and ask the HR team for a printed letter of employment - and stand next to them while they do it so that there's no chance of it getting intercepted. I'd expect them to be willing to do this as I'd wager that it's illegal to not provide one (though I'm certainly not an expert in Indian law!).
I can't believe that they'd have been told they're not allowed to give you the letter; and even if they have been, if you're friendly with them then I'm sure it'll go fine.