If I move my panel 15 ft. From where the meter is, do I need to install a disconnect outside by the meter?

Why not ask your local electrical inspector?
Google his telco and give a call... it's usually a simple
Answer.

If the cable is run outside then typically no.
If the cable enters the house and runs inside then yes.

If the service from the meter pan enters the home and goes to the service connect in the box, there is the service disconnect in the box. Why would there need to be a cut off switch. It sounds like a simple relocation of the service box.

If the service from the meter pan enters the home and goes to the service connect in the box, there is the service disconnect in the box. Why would there need to be a cut off switch. It sounds like a simple relocation of the service box.He is asking about moving his service panel.
It is my assumption that he has a main breaker panel like 99% of us out there. If he moves the main breaker panel 15' inside the structure a main disconnect would be needed outside or near the point of entry inside.

The new box will have a service disconnect. I have put in several services where the meter pan was several feet from the service box and never have I had it turned down by an inspector because there was no service disconnect before the service box or at the point of entry.But I can understand the thought process.

It's not a thought process, it's a code requirement.

See NEC 230.70(A)(1)