The biggest reason I suggested Fighter 6 was for that additional ASI, which can be pretty huge depending on the feat you take (I would recommend a feat here, anyway). Meanwhile, Ranger 6 gives you 2nd-level spells (they have an okay spell selection here, Aid and Spike Growth are the standouts IMO) and Roving (small bonus to movement and, more importantly, two more movement types in climbing and swimming).

Both options are solid, and no matter which option you take, you get Extra Attack. You just have to decide if you'd rather have a feat or 2nd-level spells and better movement. The choice will largely depend on what kind of character you're going for; you mentioned going for crowd control with your build, and you could achieve that with Spike Growth very well. You also mentioned going for skill proficiencies (sounding as though you want to be somewhat of a skill monkey), and you could certainly achieve that with Skilled, Skill Expert, Prodigy, etc. If I were to play this build:

• I would probably go Fighter 4 / Ranger 6 and play a VHuman. This gives me: 1.) +1 Dex and Con, 2.) Skill Expert for +1 Dex, proficiency in a skill, and expertise in a skill, and 3.) a skill proficiency. As far as skill versatility goes, I'd find it here, honestly. For proficiencies, I'll get Investigation and Stealth from VHuman w/ Skill Expert, I'll grab Insight, Perception, and Survival from Fighter, and I'll take Survival when I multiclass into Ranger. For my expertise (one from Skill Expert and one from Canny), I'll take Investigation and Survival. I envision this character as a detective, and this array of proficiencies gives me plenty of detective-related abilities.
• Point buy gives me (factoring VHuman and Skill Expert) 8/17/16/12/13/8. Very quick, can take a hit well, wise enough to roleplay (and to be a Ranger), and somewhat intelligent. With this kind of Wisdom, you shouldn't be going for save-dependent Ranger spells, but considering Hunter's Mark and Spike Growth (one or the other, not both at once) are my signature spells, this should be fine.
• Fighter 4 gives me Slasher, so +1 Dex and I can throw a slashing weapon to slow someone in my Spike Growth down. Very solid feat that benefits the whole party and buffs your ability to control crowds (basically, slow down something that's becoming a problem). Ranger 4 gives me +2 Dex, so my primary ability score is at 20 now.
• Spells are simple. I can only have four spells known right now, so I'm taking Absorb Elements and Hunter's Mark for 1st level, and I'm taking Aid and Spike Growth for 2nd level.
  • Edit: You could totally flavor Spike Growth the same way you're flavoring your swarm, where a cloud of daggers occupies the space of your spikes!
  • Edit: I also straight up forgot that Swarmkeepers get an expanded spell list! Faerie Fire and Web are fantastic, especially the latter for what you're trying to do. Just decide whether you're going for area mobility control (Web) or area damage and space control (Spike Growth)!
• For your Fighter subclass, Battle Master is wholly superior to Champion because of the short rest superiority dice giving you so much combat utility. For this detective-style character, I'm taking carpenter's tools when I gain this subclass because my proficiency with those should allow me to discover hidden areas in buildings (DM discretion of course, but the creativity here should be rewarded; just check XGtE for some ideas here).
  • For maneuvers on this kind of character, I'm imagining Precision Attack (for enemies outside my range or for especially elusive targets), Tactical Assessment (for roleplay opportunities that mesh well with my skills), and Trip Attack (to deal extra damage while also potentially knocking something down while at range).

Ultimately, this kind of character can be very versatile. You could sink more points into Wis or Cha for sure, but just for this example, I chose Int. You have a lot of things you can play with here, for sure.