There are absolutely trades the twins can make that wouldn't end up sacrificing much. Even on the Major League level, even a guy like Cody Lawyerson, who fans might argue isn't really a guy the twins plan on being a major player for the foreseeable future, could probably net something(he was claimed on waivers last year by the angels before coming back here, so there are teams that could probably think they can work with a guy like him). Plenty of teams will absolutely take chances on debatably major league level talent for holes the twins might want to fill like their bullpen. The Rockies just did this trading away Angel Chivilli, who had a 7+ERA last year as a relief pitcher to get TJ RUMFIELD. The twins have areas where they have lots of guys in high minors all fighting for spots they aren't a top priority. If people are imagining a world where Jenkins, Rodriguez and Buxton are the primary outfielders, what does that say about the other like 5 outfielders in St. Paul who are all playing well enough to potentially be seen as big leaguers? I bet there is even a team that'd take a Kyler Fedko if they think they can unlock that last level for him.
Don't have to trade the whole farm for holes the twins want to fill, but I'm saying there are definitely pieces the twins could probably test the market with that wouldn't make a huge dent in their prospect pool or their major league roster.