Prevent sending e-mail in Outlook 2010

Are they exchange, pop, or imap accounts?

This article says you can do it in the group settings:
https://support.office.com/en-us/article/Change-send-receive-group-settings-7184F59D-C194-44D7-973A-7AF568A918D0

You can work around it.
I did test on my Exchange 2013 but I have no option to test it on Exchange 2010 so sorry for that. You need to try for yourself

You can create Rule on your mail flow

If message is receive from:  xxxx select members from your domain

Forward the message for approval to xxxxx select member from your domain or contact outside domain


All emails from this person(s) will be send for approval to address you'll selecting.
You can see if person who has restriction trying to send message and if you'll not approve this message will not go anywhere by your designated address.


I made test in my domain
and I got message on my private email asking for approval


There is an option to apply same rule to whole group so you can do rule for group and add all users you want restrict to this group

This s only way you can do it. If you'll not approve email from this particular use then email will never be sent out.
I this this is what you was asking for,

If it is on select computers, customizing the send/receive to receive only would be my recommendation.

As detailed earlier, Outlook options on the computers for send/receive are set to receive only.  So, when a user presses F9 or the timer for send/receive triggers, only receive messages are processed and no errors are triggered.

If a user tries to send a message, the messages will store in the Outbox, but will not be sent.