Hi drwho53 - it's probably fine to just delete the shortcut but better safe than sorry since Spyaxe is invasive and can be a pain to remove.
Firstly, please carefully hover your mouse cursor over the shortcut on your desktop and RIGHT-click it (DO NOT left-click) then choose 'Properties' from the pop-out menu. In the new window that opens, make a note of the file path given in the box next to 'Target'. Then click on the 'Find target' button at the bottom of the window and let me know if it finds the target file or whether it tells you it can't find it. Either way, then carefully close all the windows without clicking on any listed programs inside the windows.
Next, if you already have the program HijackThis, please start it and click 'Do a system scan and save a log file'. When Notepad opens with the log file, go to the menu bar at the top and click 'Edit --> Select All' then 'Edit --> Copy' and finally open a reply to this topic, click to place the mouse cursor in the box and press the 'Ctrl' key on your keyboard and hold it down while pressing the 'V' key to paste the log file and submit it as your next reply.
If you don't have HijackThis, click HERE
and download the self-extracting file to your 'My Downloads' or 'My Received Files' folder (dependent on your Operating System). Then go to the folder and click or double-click the HijackThis_sfx.exe
file and select 'Unzip', letting it extract to the default folder C:\Program Files\HiJackThis. When it's done this click "OK" and close the self-extractor window. Then navigate to the C:\Program Files\HiJackThis folder, click on the HijackThis.exe file to start the program and follow the previous step to paste a log file.
As well as the log file, let me know the results of right-clicking and 'Find target' for the desktop shortcut.