If you can find the adhesive type used in manufacturing you are closer to the best possible solution (they might also suggest adhesive type proper for the repair). There can be several types of adhesives used so if you can trim down better.
Definitely if you have the veneer coming loose the faster you fix the better in the long run since larger areas are far more difficult to work and veneer accidental breaking during fixing or use might ruin your speakers not only their looks but also their resale value.
Contact adhesives that have different setting times and might or might not allow relocation so be careful. If you are dealing with small areas the provided bottle tip might not be as accurate as you might need. READ THE ADHESIVE MANUFACTURER RECOMMENDED APPLICATION PROCEDURES AND WORKING TECHNIQUES.
Normally the a containers are also designed for application as well but not be suitable for your particular job, they might designed with large areas in mind so better get some Q tips. Make some trials to learn how the adhesive handles i.e. how fast is sets (this is affected by room temperature, relative humidity so better do some trials), does it streak when you take it from the container? if so, you have to be more careful since it will tend to go outside your work area when you retrieve the Qtip after application. Better to use some paper and quality masking tape lightly applied to avoid a messy looking work if any mishap occurs. Apply the material paying special attention to edges not excesively (adhesion is a surface phenomena and excess material is detrimental to the repair success) to both surfaces to be joined ( need to be free of dust!!) keep them separated (paper clip bent as needed or some other material will do) while the solvent or water evaporates.
Then be sure of this step since normally it is not reversible and how you join the surfaces is how will they remain so take your time, think how you'll do it and go for it!!
Apply pressure evenly avoiding marring the surface and keep that way 'til the adhesive "sets" (see manufacturer recommendation) give it some extra time. Remove pressure application means masking tape and paper.
Sorry if post is lengthy. Good luck.