Interesting idea. Here's a start: What is the peak voltage at the tips of a dipole antenna?
The conclusion there is for a 100W transmitter and a "normal" dipole, you can expect a peak of about +/-900V relative to ground at the dipole ends. You'll want to pad that with a healthy safety margin. Also keep in mind that power is proportional to the square of voltage, so if you have more than 100 watts that voltage can get very high, very fast.
As the relays are closed and they find themselves somewhere in the middle of the dipole, they'll have to deal with the current. Current is highest at the feedpoint, so in the worst case, for a 100W transmitter the current is $ \sqrt{100\:\mathrm(W) / 72\:\Omega} = 1.8\:\mathrm A$. In practice lower, since the relay is not at the feedpoint. This is an upper bound.
You'll want to be sure the relays don't switch while transmitting. I'd imagine there'd be some arcing and the contacts would wear out quickly.
I suspect the bigger challenge will be controlling the relays, since being on a wire with 100 watts of RF is a little tricky. Not only do you need to get the wires to them to control them, but once you've got the wires there you'll need to devise a way to keep the RF out of the control wires and the relay coils.
I've never done this, and I can't find descriptions by anyone who has, but I might try using twin-lead as the antenna element. The common-mode current radiates as a dipole normally would, while you can use the differential mode to control a DPDT relay.
The trouble then is the mechanism to control both common and differential modes from the shack. You don't want to put common-mode RF on the feedline: that would make it an antenna. If only you had a 3rd wire...
If you use a folded dipole, you can make one. At the center of what would normally be the undriven element is "ground". You can just attach a wire there. And if "ground" is actually DC +12V, you can use that to control the relay coils.

simulate this circuit – Schematic created using CircuitLab
Of course you'll need to impedance match the folded dipole somehow, like a 4:1 balun.
You could also avoid running the 3rd wire to the shack if instead you use a DC bias on the coax and separate that from the RF at the feedpoint with a capacitor.