Well, if you delete IrfanView, I can't guess what program would open those files. Your original problem was that nothing would open them,. so I guess you would revert to that situation. You can set it up so that IrfanView will automatically open them with a double click, if you want. That is my setup and I love it.
If you go to the File types tab of Folder Options that I sent you a picture of, you will see that I have IrfanView set to open Jpg (and many other) type files. Whatever program is designated to open your files would be shown there. There is a "Change" button there. If you click that button, you will get a list of possible programs for opening that filetype. You can use this to set IrfanView to open all files of that type. You would need to set each filetype in this fashion so IrfanView will automatically open them with a double click.
An easier way would be to open IrfanView, and click the red letter "P" in the toolbar. This opens the Property folder. Click on the Extensions tab. You can select all filetypes that you want IrfanView to open. (I chose the "Images only" button which allows IrfanView to open all graphic type files (Jpg,Gif, Bmp, etc.) and it works splendidly. (There is a 'Restore' button on the File types tab of Folder Options that will set everything back to the original default setup that Windows established.)