domain name system - Changing DNS records when Moving a site

I'm building a new Magento website on a Amazon ec2 instance and will need to point domain of their old OSCommerce site to the new ec2 instance's elastic IP address.

Normally I would have though this a simple task of updating the A record of their domain, but when I logged into the account with their register I see they have 90 records set up already, mostly CNAME & A records.

They have no IT guy to ask, but I'm almost 100% sure what I need to do but as I normally work with web dev stuff like php and javascript etc I just want to make sure I have it right.

To give you a sample of their DNS records they have set up:

Type    Host                            Data                        TTL      Kind    State    In Synch
A       intweb1.their-domain.com        19?.??.???.OLD              3600     Manual  Active     yes
CNAME   intweb.their-domain.com         intweb1.their-domain.com    3600     Manual  Active     yes
CNAME   www.their-domain.com            intweb1.their-domain.com    3600     Manual  Active     yes

A       fs.their-domain.com             19?.??.???.OLD              3600     Manual  Active     yes
CNAME   fileserver.their-domain.com     fs.their-domain.com         3600     Manual  Active     yes

I believe I only need to REMOVE:

A       intweb1.their-domain.com        19?.??.???.OLD              3600     Manual  Active     yes

AND CHANGE:

CNAME   www.their-domain.com            intweb1.their-domain.com    3600     Manual  Active     yes

TO:

A       www.their-domain.com            19?.??.???.NEW              3600     Manual  Active     yes

AND ADD ANOTHER RECORD:

CNAME   their-domain.com                www.their-domain.com        3600     Manual  Active     yes

Is this correct?