War weariness isn't a problem if you manage it properly.
Ie, if you are in republic / democracy and choose to go to war, then you should only do so knowing you have the resources to meet your objectives quickly and make peace again (take a city / resource, stop an enemy army etc).
Especially at Emperor level, I find the AI will declare war for any tiny reason, and you certainly don't need privateers to get the AI grumpy with you.
The thing is, bang for your buck, privateers just don't measure up to frigates. Sure, you might be able to take out some loaded galleons, but you will take heavy losses with privateers, and how often do you get the chance to attack an undefended loaded galleon?
Instead of fluffing around with peacetime sneakiness, you are better off investing in a solid fleet of galleons and frigates so that you can protect yourself in the event that the AI declares war on you. With Frigates you can confidently sink his galleons, protect your galleons and bombard his coastal roads.
Privateers are average at best in times of peace, but in times of war, you will wish you stuck to the traditional navy. I'm not saying I never use privateers, because I do. But their use is very limited, and they just aren't reliable enough to build any sort of strategy on them.
I will grant that privateers are FUN. It's pretty cool forming an alliance with someone and then screwing them with privateers behind their back. And the enslave ability is inviting too.