Lowering TTL on nameserver, not registrar, then changing nameservers?

A better way to accomplish what you want might be to, if possible, match the records in both name servers then switch the name servers first. That way no matter what name server the client gets it will give the same answer.

Then when you're sure the new name servers are working you can lower the TTL there and switch the individual records.

Also, since the fqdn of the name servers will likely be different, I think the time it takes for clients to make the switch will be affected more by the time it takes the registrar (GoDaddy) to make the change with the root name servers than the TTL of the NS records themselves.