It would be helpful to provide some pictures of the whole shower installation.
The part you are working on could be either at a low or high position. I think I see the edge of a ring for some sort of fixture to the right. So low is likely. If you do not have a fixed shower head and a source control, then this is your source of water for a hand held only. I don't see a control, so the shower is likely configured with only a hand held and the flow control is on the hand held device. There are two ways the device you are working on can attach. I can be soldered to a copper pipe behind the wall or screws into a female device behind the wall. If it is soldered (sounds like what you may have) making a hole in the wall to change things is required. If it is screwed in you can replace it. But your effort points to soldered.
You need to determine what/where all the pipes and valves are located. But if what you show is all you have; you are going to need to make some serious changes. There is no point trying to unscrew the handheld water source. you can't make that into a fixed fixture valve. Well, you could use the existing pipe behind the wall and put in a control valve or screw one into the divice you are trying to remove if it will fit. But probably easier to just use the handheld and use it for the shower. The simplest approach would be to get a vertical bar and a handheld with an adjustable clamp and run the head up to the top for regular showering. This lets you do both fixed shower head and handheld from the same handheld device. You may need a longer hose. Shower head will all fit on the device you have now.