How to better specify kindo fo ID in RESTful service

I'm looking for an opinion about defining contract for standard GET/PUT/POST/DELETE methods.

We have resource, let's say Client, so route will be /clients

However, we have two types of id for the client. One is the ID generated by our system. On top of that we want optionally allow customers use external id, generated by customer themselves.

So, if customer never going to add clients to the system, don't really interested about integration, and need only use method GET to read customer, endpoint will be:

/clients/{id}

However, if they want full integration, with ability to add clients, and use some their id, we want give them ability to use their own id.

We considered four possible solutions:

1. /clients/external/{externaId}
2. /clients/ext-{externalId}
3. /clients/{externalId}?use-external-id=true
4. /clients/{externalId} with additional header -"use-external-id": true

We are leaning to options 3 and 4 (can be supported simultaneously) but concerns about "restfulness" of such approach. Any opinions on this? What would you choose and why?