Yes, wireless keyboards have been around for years, and their latest generations have improved greatly in both robustness and efficiency, but the best models tend to be quite expensive. If you have a USB keyboard and would like to get rid of its cable entirely, a good option is to turn it into a Bluetooth keyboard. The modification shares several points with the process that converts PS/2 keyboards to Bluetooth, and in addition to eliminating the physical link, it also opens a path of compatibility with mobile devices.
One of the main problems faced by those of us with a certain preference for PS/2 keyboards is the loss of compatibility. Computers and mobile devices have more compact designs and greater integration, which requires eliminating interfaces that the industry sooner or later declares obsolete. In the specific case of PS/2, some manufacturers offer hybrid designs where a single port can be used with keyboards or mice, but most have directly removed the port in favor of a greater number of USB connections. To this we must add the arrival of mobile devices. It is assumed that the USB OTG specification allows connection of USB peripherals without having to convert or reinterpret signals; however, not all OEMs enable OTG mode, leaving us only one option: Convert our USB keyboards to Bluetooth.
Building the converter
The DastardlyLabs channel on YouTube published a two-part video series teaching us how to build our own USB-to-Bluetooth keyboard converter. While prebuilt modules exist that could save us several steps, this tutorial takes the route of the Arduino Pro Mini, coupled with a USB host shield, a Bluetooth module with its firmware hacked to function as HID (at this point it leads us to another tutorial where we can do that step by step), two small compatible RS232RL and FT232RL programmers, some perfboard, and a good number of pins. The host shield must be slightly modified to work at 5 volts (essentially cutting a trace and making a jumper), and of course the firmware must be loaded onto the Arduino before making the connection.
Powering the converter
The last step is to provide power to this converter, and that's where the user has some flexibility. We'll need 5 volts, so the first thing that comes to mind is a pack of emergency batteries (external and easy to recharge), or something along the lines of a system with lithium batteries and its own charging circuit. I want to stress that there are more direct solutions, such as the Bluefruit EZ-Key that was used here to convert an old IBM Model M to Bluetooth, but there are budget and parts availability issues that cannot be ignored.
Source: DastardlyLabs YouTube channel
Source: Hackaday article