I wouldn't do any of the things you mentioned because they all put you at risk of being attacked or blunderbussed during an emote. Just a personal preference, though I get where you are coming from with the cannons up and emoting.
Instead, as much as I hate to say it, use the "We're Friendly, Let's make an Alliance!" option from the megaphone as soon as you get close enough, and repeat it once if needed in case you weren't actually in range, not more.
If the ship is moving toward you very quickly, use "Friend or Foe?" after and if there is still no response and they are in chainshot range, you open fire.
Of course, using your mic is also a good option, but the prewritten dialogue translates to different languages so I always use that too just in case.
When you are the one approaching, stop at a distance from them, prepare a prewritten message (if you are on PC), and you can actually keep the message until you are ready to send it. Shoot over and then immediately send your friendly note and sit by your mermaid. Never board without permission, and of course something like lantern out blinking can sometimes help. Better than having a gun drawn at least.
I too enjoy making alliances, which is one of the reasons I play solo sometimes. It is a lot harder to make unilateral agreements with other ships and keep your word when you have a larger crew (who egg eachother on to betray, steal, etc).
Happy there are other pirates out there who appreciate the art of diplomacy.