asterisk users - Sep 2013 - Setting different caller-id for second leg of the Originate

Hello all,
I would like to set a different caller-id for the second leg of a call
when doing an originate.
For example:

Action: Originate
Channel: sip/1234
Context: mycontext
Exten: 1
Priority: 1
Callerid: "123 <123>"
Async: true

This sets the caller-id correctly when dialing sip/1234, but I would
like to set the caller-id for the second leg of the call (the one that
goes to 1 at mycontext) to something different. How do I do that? Would
it be enough to change the caller-id as soon as the call is
successfully connected?

Thanks for any pointers,
l.

PS: I Know one can easily do this by editing the dialplan at
1 at mycontext, but this is something we cannot do now.