That smaller tool is a lockring tool, not a freewheel remover. They are not the same thing. Even in Italy, Shimano components and tools are very common. Freewheels require a lot of torque to remove, you absolutely need the correct tool to get them off. I have seen freewheels that took huge amounts of force to remove, no makeshift tool is going to work. Every major bike tool maker makes a tool that can be used to remove your freewheel. Park tools are common in North America, maybe not so much in Italy. Cyclus and VAR tools may be easier to find where you live. Any bike shop anywhere would have the needed tool. You only need the tool to remove the freewheel, you can thread it back on by hand. Perhaps if there is a local shop you could take the wheel in and have them remove the freewheel, only takes a minute or so