You do not need a wireless router, or any other wireless devices, to get Mingle XP - just put the DS in mingle mode and leave it on overnight (might be a good idea to plug it in to the wall while you're at it). At random intervals over periods of several hours, bizarre and random encounters will show up to give you XP (can't remember any off the top of my head). These are produced by the game without any other wireless devices being nearby. Aside from battle XP, this is the fastest way to get XP (faster than shutdown).
You will need mingle XP to get 100%, as some pin forms will not evolve (or will not NOT evolve, since both battle + shutdown will evolve it, and you need every pin maxed to be at 100%) without it. At some point you may want to check out the TWEWY wikia, which has maps of all the pins and which forms will evolve them...it's kind of like the Pokemon games - yeah, you COULD play them without a strategy guide, but it's going to be kind of frustrating without a comprehensive list of which guys learn which moves at which levels, and which other guys they can breed with, and so forth.