This is a common problem for those who want to use a soundbar as it takes an available HDMI port. When you say you only have one 4K port, do you mean HDMI 2.1 since even older HDMI ports can support 4K, but not all of the 2.1 features (4K 120Hz, VRR, etc). What TV are you using?
As for the HDMI switches, what you have linked is a matrix which I don't believe is what you would want as that is for taking multiple inputs to multiple outputs, while you only have a single output. Something like this should work though:
I haven't tested or used a switch like this, but the reviews seem positive.
It would be super helpful to know what switch you got so we can help identify what issues you may be running into. It is important to have a powered HDMI switch and that it is at least HDMI 2.0 with 18Gb/s bandwidth. There are tons of these on Amazon with relatively good ratings. As well, you need to be using 18Gb/s HDMI cables as a absolute minimum.
This isn't a guarantee, but more of a general rule.
I would likely consider something like this...
https://www.amazon.com/HDMI-2-1-Switch-60Hz-Projector/dp/B0B639RRJ3/ref=sr_1_1_sspa