If our company has 2 domains (same ownership & address), will only the alternate domain be at risk with cold email campaigns?

That is correct. With cold email even if you are reaching a targeted audience with a relevant message, over time inevitably some portion of recipients will mark your email as spam. 

One possible solution is making sure you are using as many mail merge data points as possible so that your recipients can feel that the message was written specifically for them.

Here are some custom merge field ideas that can help to craft more personalized emails: 

• How/where you learned about their company
• Company name
• Industry
• Business type
• Service they provide
• Their locality
• Any common point shared by campaign contacts