I tested some and it looks like you can't fix this with Skype for Business. When you use the Suppress caller id in Skype it will add the number you set to P-Asserted-Identity in the SIP INVITE, your operator will use this to mask the call.
When you do a Simring call or forward call Skype will add the User 1 phone number in the P-Asserted-Identity field in the SIP INVITE, so it will not use the suppress caller id.
If you have an SBC connected you might be able to change the P-Asserted-Identity with the SBC.
With the configuration you have User 2 will be able see that it is User 1 that is calling so it is easier for User 2 to call back. Also if there is an external user calling User 2, that user will be able to see who is calling.
Best Response confirmed by
Mikael_J (New Contributor)