Another DNS problem

Hopefully this hasn't been answered somewhere else, but I've looked around and haven't really found a suitable answer.

I'm looking to change web hosting providers, currently we have it setup with our ISP that provides our T1 line. Our DNS records are setup with NetworkSol pointing at our ISP's nameservers they provided us with. My problem is our mx record sends the mail to our exchange server. I want to be able to update my nameservers without disrupting the mx record so that we don't lose our current e-mail setup (we are not changing ISP's just getting a new web host) but people will be able to access our website on the new host. Is this possible to do, or will I have to change the exchange servers setup as well?

Sorry if this doesn't provide enough information, this is definitely not my usual area to be working in.

 

 

 

 

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