Oh, I recognize that name. Trichlor - yes, you could use some while you are away.
Unless you plan to leave your pump running 24/7, don't put the sticks in the skimmer. Use a floater instead. If you use a floater, you can't use the solar cover, so you're neighbor will need to watch the water level (evaporation).
If you do decide to use the sticks, they will raise your CYA level some, but I think you're at 40 now, right? So that's okay, it won't raise it too much, though you didn't say how long you'll be gone? Just remember to retest your CYA level when you return and adjust your FC levels accordingly. Also pucks are acidic so make sure your TA is at least 120 and the PH 7.8 before you leave. (I didn't skim the thread for those numbers, can't remember what your's is now.
If you decide to forgo the sticks, just throw on the cover and have someone add bleach for you, you'll be fine.