Sfdcfox answer looks fine to me, however I have some remarks to point 1. and it is quite an improvement so I decided to not leave it as a comment but as a seperate answer, because some people may find it more useful.

The problem with overriding default layout is that it's very hard to maintain-everytime you want to add the new field to object you have to modify VF code. There's however an alternative:

• Create custom VF page displaying only button
• Make the rendered attribute user-dependent so it only shows to certain users
• On the standard layout of object create a new section at the top with blank header and put your VF page there

The advantage is you still have the rest of the layout in standard SF and if the button is not visible you just have a bit of margin between standard buttons and rest of the layout.

Sfdcfox' answer looks fine to me, however I have some remarks to point 1. and it is quite an improvement so I decided to not leave it as a comment but as a separate answer, because some people may find it more useful.

The problem with overriding default layout is that it's very hard to maintain  - every time you want to add the new field to the object you have to modify the VF code. There's however an alternative:

• Create custom VF page displaying only a button
• Make the rendered attribute user-dependent so it only shows to certain users
• On the standard layout of the object, create a new section at the top with a blank header and put your VF page there

The advantage is you still have the rest of the layout in standard SF, and if the button is not visible, you just have a bit of margin between standard buttons and the rest of the layout.