Wine can usually be installed from the main repository of most distros (Mint repository, Ubuntu one...). I don't know if speccy is the sort of software that can really be handled by wine, it is designed to gather low level system details and I don't know if it does this in a windows specific way, furthermore it might be the case that only older versions of speccy can be run like this (Wine seems mainly optimised to run windows programs from the XP era). Anyway, below I've put some tips about installing wine, but generally for installing windows programs with wine it is best to see if you can find program specific instructions by someone who has tried it before for the program you want to install.
First download wine from your relevant repository
then run the terminal command sudo apt-get install winetricks
winetricks can make installing programs under wine easier
you might need to configure wine by running winecfg in the terminal and setting the version of windows you want wine to act as (xp,7,8,8.1,10...)
then try opening the installer exe file for your windows program using by going nto the folder where you have saved the exe file and using "open with-->wine windows program loader" which should be shown as an option for .exe files once wine has been installed. Click through the installer and hope it works, if not search online for tips about your specific program, in your case speccy, on wine. If your program installs ok then you should be able to see it installed in the "wine" or "other" section of your linux applications menu. You can also usually run programs under wine by doing
wine "C:\Program Files\wherever you\told the\installer\exe file\to put\ the program.exe"
in your linux terminal. That file path is based on where the exe file required to run the program (different from the installer exe file) would have been put if installed on a windows machine, so some sub directory of "Program Files" or "Program Files (x86)" usually. You will probably have seen this as the default file path while you were working through the installer.
Personally I use wine for running Google Sketchup 8 and Notepad ++ (whatever version was latest in October 2017), it works well for these on Linux Mint 17.3 and Ubuntu 16.04 LTS computers though there are some small bugs and launchers and links to wine programs can be a bit unreliable for me.
The wineHQ database tells you about programs people have tried under wine and what tweaks they have tried, I haven't looked in great detail but here is the page for speccy on wine, it doesn't look too hopeful, most speccy versions are considered "garbage" under wine (won't run at all) and the best luck anyone has had yet seems to be a "bronze" rating meaning some aspects may work if you are lucky. https://appdb.winehq.org/objectManager.php?sClass=application&iId=12584
That said the latest tests on their are quite old, things might have improved since.
Another option is PlayOnLinux but I have no experience of this at all.
Edited by rp88, 08 April 2018 - 11:52 AM.
Back on this site, for a while anyway, been so busy the last year.
My systems:2 laptops, intel i3 processors, windows 8.1 installed on the hard-drive and linux mint 17.3 MATE installed to USB