It's not as bad as you think it is. As someone else has already mentioned: take a campaign where not many players will be. For example: before you PvP, you have to select a campaign. So, in the list of campaigns, scroll down to the bottom and take the last campaign. Most likely there will be very few to no players.
Another option is to take a group of 5-10 people and go explore the PvP world to hunt for skyshards. In the meanwhile you can enjoy the beautiful landscape xD. There is also quite some PvE objectives you might be able to complete with your group. (still in that low to not populated PvP campaign).
You don't have to "create" a sneaky character. Wherever you are, whether it's PvP area or PvE area, just press "Ctrl" and you will be crouching/sneaking (this means you are invisible, until you come to close to enemies).
So, there's no need to panic! I think ZoS made a good deal on this.
Anyway, enjoy your Tamriel adventure nevertheless!