For the installation of plastic buttons you can make yourself the nozzle.

In this case, use the nozzle to install the alpha buttons with a diameter of 12 mm.  
On a lathe grinds the tip of the nozzle (manually will not work)

Get a new nozzle for plastic buttons with a diameter of 10mm, suitable for installation details "Papa" and "Mama."                
                                                           
          As the lower nozzles use the stand to install the buttons with a diameter of 10 mm or 12 mm.
               
Such a nozzle can be set any diameter plastic buttons. Checked, I bet.

Example: buttons with a diameter of 12.5 mm      
Note: the nozzle has a diameter of the rod a little more than 4 mm.

                       When setting buttons with a diameter of 9.5 mm it is part of a very tightly button, so you have to be very careful when installing. I recommend to make two heads: one with a diameter of 3mm (for buttons with a diameter of 9.5 mm) and a diameter of 4-4,5 mm (for buttons with a diameter of 12.5 mm).

Attention:

Do not conduct experiments on the product of the customer. First, check the installation details button on scrap piece of fabric to achieve the required result and only then go and execution of the order.

To be continued.