Is map iteration sufficiently random for randomly selecting keys?

Can I rely on the random iteration order of maps to implement a random "pairing" of clients in a web application? I've tried looking around but can't seem to find a breakdown of how random this randomness is.

The algorithm would look something like:

var clients map[Client]struct{}

func PairClient(c Client) (Client, error) {
    for m := range clients {
        if m != c {
            return m, nil
        }
    }
    return nil, fmt.Errorf("lobby: insufficient number of clients")
}

Would this be sufficient when there are >1000 connected clients, or should I maintain a separate slice of clients and randomly select from that?