I have my mail server installed on local machine with everything works fine and smooth. My IP is clear from all the blacklists as well. Emails come and go perfectly without being landed in SPAM, which is the best part

I have a newsletter app running from a shared hosting with its IP address blacklisted. Emails from my newsletter app (interspire) goes to my mail server and then transported to the final recipient.
Now majority of the emails from my newsletter app are being marked as SPAM... because my shared-hosting server's ip is blacklisted ....
I need a way to replace ip of my hosting server with my mail server's ip. So all outgoing emails will be received as if they were sent directly from my mail server.
This is how header look like :
Received: from mydomain.com (myhostingcompany.com [50.31.160.55])
by my.mailserver.com with ESMTPA
I want a way to completely replace/change details about my hosting company because that is what's getting my emails into spam.
My mailserver has proper domain key, spf record to include ip address of my hosting server's ip as well as my mailserver's, rDNS / PTR all set.
I am using HmailServer 5.6-B2145
I am not a programmer so please help me in details if you know how to get this working.
[I do know that I can install my newsletter app on a local machine or on mailserver pc and get the results I wan, but that is not an option here with me, so I'm restricted to the scenario mentioned above]