Fortunately, I now have this great device with which I can connect all three devices to one HDMI output on the TV. The installation is very simple: the supplied batteries into the remote control, connect the chic black box with an HDMI cable to the TV, which connect devices with HDMI cable to the box, plug in the infrared cable into the box, ready.
(The HDMI cable required will of course not supplied. To connect three devices you need four cables.)
Switching is a little slow, but I'm happy to take into account. More importantly for me the picture and sound quality, which is not reduced by the intermediate box at all.
I am completely satisfied with this small technical assistants and am pleased that I have to reposition no cables.