Question about erminating Manged DNS service and alternative options for existing forwards?

We have a couple of internal DNS severs. We also HAD our www.website.com and pop mail hosted by Hostway.  We no longer have them managing our website nor administering our pop mail.  I have an internal exchangeserver 2003 behind my network (yeah i know behind the 2007 curve/hoopla) and our website is now maintained and hosted by a different design company.  Hostway claims that if terminate our contract with them and just keep the domain registrations with them we loose the access to their Domain Managment section where I have our site and my MX record forwarding to the public addresses of my website and exchange.  I am trying to figure out an alternative without breaking functionality of these two resources?  Any suggestions.  The web-design company we are now using has no DNS management services, just their internal servers they say, and I don't believe using my Internal DNS managers will work/is best practice?

Any clarity and/or options/input would be appreciated in how I can move forward in dealing with this!!

Thx