You cannot do this directly since the security permissions would exist even for the web services. You could however achieve this using a middle man, or application in the middle.
Here is how it would work, and actually I can think of two potential ways to make this work.
1. You would create a separate web-service application on the CRM server in a different website (but on the same box) that allows client script calls. Now you can send soap envelopes to that service from the jscript behind your button, that app would
use a different user context or impersonation and call the web service methods you are looking for.
2. You could probably create a custom entity and give all your users write access to it, then you could illicit an update call on that entity (could be on any instance of the entity) using a jscript call from behind the button. You would attach
a plugin to the update message of that custom entity that used impersonation or ran in a different users context to then perform the claim action against the web service.
I hope you find this helpful.
Jamie Miley
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