Most of the mass market records come in printed inner sleeves like that which I don’t believe are intended for long term storage but for the edification of the listener with liner notes and or lyrics.
Instead of any kind of wet cleaning I would use a good quality CF brush while spinning the turntable platter unpowered not more than one revolution and then sweeping the line of debris collected to the edge of the record. Acquire a silicon roller, I personally use an "In the Groove" starting with the top of the record label at 12 o’clock, roll first down the left of the spindle from the top toward you and then to the right of the spindle. It will take multiple passes lifting the roller to ensure complete coverage. Then rotate the platter a quarter turn and repeat the process.
If you have the surface of the record properly illuminated, you will see the effectiveness of the roller’s ability to remove the marks left by these sleeves. In addition, if you concentrate with light pressure the rollers edge in what look like particularly troublesome areas it will literally lift imbedded matter out of the grooves. Though it’s not fool proof, I use this method with every new record and somewhat less intensively with every record I play.
I will add that after the first play you should repeat this process before turning the record over because your stylus which is really the only way of contacting the most intricate surfaces of the groove will push any remaining matter in the groove to the surface of the record which you can immediately remove with the roller. Your next play will be even quieter!
Reserve wet cleaning for used record purchases and keep it simple and only do it once. If it doesn’t result in a comfortably quiet surface, return the record. Spin Clean following the manufacturer’s instructions implicitly works almost every single time.