When you say "alcohol inks", do you mean those small dropper bottles, that are sold in packs of a dozen different colors in craft stores?
The short answer is, yes, they are perfectly safe.
You can probably stop reading here, but I'm going to need to write a longer answer because that's what's expected on this site.
The alcohol inks that are sold in craft stores contain an extremely dilute form of alcohol, with only a small quantity per bottle, meaning that there is very little of the active ingredient to aerosolize or evaporate during ususe. So the fume risk is minimal close up, and negligible at a distance of more than about a meter.
Evaporation data (not identical, but a near enough equivalent for what you are doing).
The small opening at the top of each dropper bottle also minimises evaporation.
This means that an individual can safely sit with them for an extended period of time in a room with only moderate ventilation and no respirator or mask, as the active ingredient will never reach a volume that would be harmful to them.
You would only be at risk if you had people using them in a small room with no ventilation, and you were using them in a way that deliberately aerosolized them and they had their face inches over it. For example, if you were airbrushing them in the cupboard under your stairs.
Even then, it would likely only give you a mild headache.
The warnings mostly apply to industrial or commercial use, where you have hours of exposure to highly concentrated inks. Such as in a print studio.
I personally use them to dye resin, and have been doing so for some time. They are mostly alcohol in name only, the biggest problem is them staining things, not from the fumes.
It goes without saying, don't drink them.
On the issue of safety data sheets. I deal with them on a daily basis in a processional capacity, for industrial chemicals that pose a danger to health, and I have the appropriate training to do so.
For crafting inks, safety data sheets are a statutory requirement and are there to limit liability, not to serve as guidance for use. They don't cover volumes, dilutions or use cases.
The same safety data sheet is used for a dropper bottle as for a 50 gallon drum. In the same way that a tree and a toothpick are essentially identical as far as statutory documentation is concerned, but having one dropped on your foot would have a very different effect from the other.
Or, to put it simply, if you're using alcohol ink in an industrial quantity then apply industrial safeguard. If you're using it at home, then crack the window open and stop using it if you start to get a headache.
Or, to put it even simpler, it's perfectly safe, so long as you don't repeatedly sniff directly from the bottle.