Hi Carver - I've not had to replace my solenoid, but I can't see why you couldn't do it with the top up. That's certainly the way I'd do it.
However, I'd cut 4-2x4s to the same, appropriate length and place them between the 4 outriggers on the bottom half and the lower edge of the top half, lowering the top half on to them so that they support it BEFORE you start working on the solenoid. You can use duct tape to hold the 2x4s in position before you lower the top on to them. Once they are supporting the weight, you can be confident that the top will not suddenly drop on you while you are working. I would NOT depend on the safety bar to keep the top up for this work.
No, there's no fluid in the solenoid, but it IS connected directly to the battery, so that is another thing you should actually remove from the trailer before you start fooling around with the electrical connections at the solenoid. You could easily get around 50 Amps of current in a spark if you touched something wrong with the battery connected. Get it OUT of the trailer, so there's no danger of that happening.
If I've given any bad advice, someone will correct me, I'm sure.
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew