One-wide swap red stone wires vertically?

Solution 1:

Since you apparently don't want moving parts (which eliminates solution 1 and 3) and being able to send a signal through both wires at the same time is a case that can happen (which eliminates solution 2), I worked out yet another solution.

Like the first one, it's 4 wide tileable for 2x2 wires. The idea to this is actually pretty similar to the first one, I just let the wires go around each other while avoiding that they power each other. The piston was an easy way to do that, since it can go down without going forward and only one redstone wire of the other path had to be replaced with a repeater to avoid problems. Without the piston, I had to use more repeaters and some clever wiring.

Here is a screenshot of all eight lines that you need:

Since that's not very helpful for rebuilding, you can download the structure file here*.

The odd numbered (counted from the left) columns have one redstone tick delay, the even numbered columns have three redstone ticks delay. I tried to switch one repeater over from the even numbered column to the odd numbered column, but that didn't work, because all three repeaters on the even column are there to avoid power overflow between the two lines of the even column. If the difference in delay is a problem, you can fix it by just putting two repeaters on first setting in front of the even numbered column lines.

It's 8 blocks long, 5 blocks high and of course 4 block wide for 2x2 wires, which makes it more compact than my first solution, but there are less air blocks, so you actually need a similar amount of material:

You need 28 redstone, 8 repeaters, 1 slab and 42 blocks that support redstone on it, some of them have to be solid, so you should build it all out of solid blocks to be sure, except for the one slab of course (that's not included in the 42 blocks).

This design works with pulses of any length.

Late edit: You can replace the repeater in the odd top input->odd bottom output line with a piece of redstone dust, but since that makes the delays even more varied, I won't edit that.

*That file is on my Google Drive, but it shouldn't get deleted. If I accidentally delete it, contact me (contact details on my profile page) saying that the file is in my October 2017 backup and link this answer.