I'm trying to remove the clouds from the picture as cleanly as possible while keeping the wires still visible. What I'm aiming for is the structure with the sky cut out. I'd rather not make a path because it would be really tedious and the shape would be very complex as there are lots of lines. Any help would be greatly appreciated!
Have a look at the picture's blue channel. The dark areas mostly correspond to the tower and cables, while the bright areas are sky. You can create a selection from the channel (Ctrl + click on the blue channel), invert the selection, and turn the selection into a mask.
It may help to first duplicate your photo, add a solid white layer underneath, and apply the mask to the duplicate. You can then fill the areas of the mask that you need solid (the building canopy and tower).
Before making the mask, you can also enhance definition by using adjustments (especially Levels) or blending layers (e.g. a 50% gray layer set to Linear Light, tweaked with dodging/burning).
You can use another layer to reinforce the cables (such as with a 1px Line tool in Pixel mode at 25% opacity), or even replace them.
That answer might not be what you want but if this was my project, I would isolate the easy elements, and then trace back the wires. It's quite easy if you hold the shift key from one point to the other to trace straight lines. You can also do that part in Illustrator.
That picture is very delicate and trying to cut out the wires or using channels or levels will still force you to re-trace some parts of the them anyway. It's almost easier to trace them back than doing 10x manipulations on your image; the result with be sharper too. All the solutions possible to cut out the background will require some patience and skills.
Use a layer mask to isolate the obvious elements like the mat, roof and people.
Whenever possible, avoid the magic wand tool; it does a very sloppy job. Wand tool is ok for joke montages of your friends like sticking a squirrel's head onto someone else body, but not for real precise masking. You can ignore the wires if they're too hard to isolate for now and mask them. Keep those triangle parts that join the wires together or redraw them too if you prefer.
For the wires, you'll need to trace them on a different layer. You should a duplicate of your original picture without the mask to use a guide. I suggest you trace the wires more at the back on different layers than the ones at the front. This way you'll be able to adjust easily your colors and thickness, and even add some transparency to make the effect more realistic.
Use the colorpicker tool to get the exact color of each wire and find the right size of brush/pencil. Use a hardness that is around 70-80 to add a blurry effect and not make the wires too sharp. A lot of the wires have the same thickness, it shouldn't be too long to adjust yourself for each of them.
First duplicate the image. Try with the magic wand adding every slice within the cables, it's a bit tedious but with the right tolerance it should work.
If the cables are too thin you can duplicate the layer and try to adjust the levels or merge several copies in colorburn, or other options in order to make the cables thicker. This is just for the wand selection... once you have a good selection you can feather the borders and erase the sky.
I would consider some "cable loss" or blurring in the thinnest cable as unavoidable