Thank you for the report. Have a look at the If your router supports Wi-Fi Protected Setup (WPS) mode, try to connect through this mode: section (1. to 3.) in the HP LaserJet Pro MFP M28-M31 Reference Guide (http://h10032.www1.hp.com/ctg/Manual/c05672924.pdf) for WPS.
Do not use a direct Wi-Fi connection from a computer to the printer. Instead, as mentioned earlier, connect the printer and the computer to a Wi-Fi router. WPS is one way of doing this.
I assume that the HP software is mainly for setup purposes. In addition to this, it may be a way (for HP) to monitor the printer (ink supplies. et cetera). Only you can decide whether such software is necessary/wanted.
In many cases, the setup can be done manually as well. This printer appears to contain an embedded web server (EWS).
See the Method two: Open the HP Embedded Web Server (EWS) from a web browser section on page 41 in the User Guide (http://h10032.www1.hp.com/ctg/Manual/c05847830.pdf).
A configuration report can be useful (see also the Check the Wireless LED status from the printer control panel: section 2. in the Reference Guide).
It should be possible to connect an external optical or flash drive to the computer (with the appropriate adapter), if necessary. Usually, software (if at all required) can be downloaded directly to the computer from the printer manufacturer.
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