Buttons are made from a lot of different materials. Even plastic buttons are commonly made from half a dozen different kinds of plastic. Some of these are easy to glue and some are difficult.
Weldbond sticks to a lot of stuff, but plastics are among the things it doesn't bond well to, especially some of the plastics some buttons are made from. So adhesion would be hit or miss. It might well be adequate if the finished work is protected, but you might find that some of the buttons fall off if they are handled.
Hot melt glue might work, especially if you can get some into the holes. Some of the harder-to-glue plastics bond better with heat, and if you can get glue into/through the sewing holes, that would give it an anchor.
But let me suggest a non-glue solution. Variations on the Buttoneer theme have been around for many decades. Similar mechanisms are used for retail tagging, quilt basting, etc. Basically, a nylon filament secures the button, either by looping through two holes and locking behind the fabric with a toggle, or there is a knob on the button side larger than the hole and you use one fastener for each hole. Most are inserted in one quick action by loading a strip of fasteners into a "gun", inserting the gun's needle(s) through the button and fabric, and squeezing a trigger to insert the fastener.
Buttoneers basically suck for their intended purpose of fastening working buttons to clothing. Especially after the fasteners have been through the dryer a few times, they get brittle and break. They will also break if you use them for buttons that will be stretched, like a pants waist. However, artwork isn't exposed to the things that causes the fasteners to fail. Attachment with a Buttoneer will be faster than glue, the result is finished as soon as you remove the tool (no drying time), and if you need to remove or move a button, it's trivial to snip the fastener (glue will leave a mess).
There are currently a number of variations on the insertion tool, like these (all pictures below are from Amazon):
The tools typically come with an initial supply of fasteners and you can buy bulk packages of the fasteners. The fasteners are generally available in clear, white, and black, and sometimes a few other basic colors, like brown, so there are some choices to minimize the visibility of the filament.