A good power strip switch should be able to handle the load you mentioned. The power strip will normally be switched On with the load mostly low on a ZW transformers as the trains will not be running. The switch on the power strip is probably rated for 10 or 15 amps and will easily hold the lower load while running. trains. I am a big fan of power strips and have them on stereo systems to save receiver switches and make unplugging when not in use to protect from lightning.
It is good to use a power strip for train transformers as once they are phased by transformer plug orientation, they will stay orientated when switched On and Off with the power strip switch and when the plug of the power strip is removed and re installed. The other lighting transformers can be phased also and stay that way when on the same power strip. This will allow you to use the came "common' for trains and lights and may reduce running separate "common" for lights and tracks. This the way I wired my 44 year old layout with three LWs and three lighting and switch transformers. I like to keep it simple, easy and economical.
If I understand your last question you are planning to operate trains with the ZWs and also the lighting. voltage. I would set the small levers B and C at 12vac for lights and 14 for switches. My only cautions would be if the levers are accidentally moved when operating trains with the A or D levers and to check that 12vac is set must be checked with a VOM meter or if a volt meter is installed.
As I stated above I have separate small 40 or so watt transformers for lights and switches (I have 31 on the layout.) I did this as the LW has 125 watts input power which is great for one train operation and in fact more wattage than the ZW for one train. But I have a couple of 2 trains on 1 track relayed systems and the LW, 125 watts is a little low for running two trains at a time. Therefore, I decided to let the LWs run only trains and I added two 12 volt lighting transformers ( as they have a steady watt demand) and one switch transformer ( which is a momentary demand) to take those loads off the LWs. It is easy to find low ( 20 to 40 ) wattage 12 vac transformers at garage sales from out door lighting system or other applications.
Since you are in the building the layout phase you may be interested in my OGR post below that shows and tells how I built my post war toy Lionel and Marx layout. The post has a table of contents at the bottom of page 1 and post 1 so you do not have to read through 8 pages of posts. Pg 1 and post 1 should show up first if you hit the link below.
https://ogrforum.com/...ra-027-layout?page=1
Charlie