Follower of the Way
That's within the ballpark, yes.To me, it sounds like you want it where a swordmage can perform magical combat maneuvers. The swordmage makes an attack with their sword, and something magical happens at the same time.
Perhaps, to help the explanation, it would be good to note that I would prefer that Paladins, Rangers, Psions (or whatever we call them), and (possibly) Shaman not cast spells. That doesn't mean they shouldn't have supernatural abilities, mind. Just that their supernatural power should not be the narrow, highly specific thematic-mechanical structure that is "spellcasting." So I would likewise want Swordmages to definitely use magic (it's right there in the name, "mage"!) but NOT cast spells in the sense of having a set of slots, preparations, etc., etc., instead having something like magical maneuvers that are skill and supernatural combined.
I should also clarify, I would not want the Swordmage to be incapable of bringing non-combat utility. I would just want that utility to be rooted in the same source as their skillful utility. E.g., perhaps an intermediate (e.g. level 5-9?) combat technique could be "Ethereal Lunge," allowing the Swordmage to leap through solid obstacles to attack an opponent on the other side. Outside of combat, one could use this as a limited form of teleportation, with the distance you can teleport defined by your movement speed or some multiple of your Acrobatics bonus (whichever is higher), and the number of people you can pull along with you defined by (say) half of your total Athletics skill bonus.* (A supernatural effect, yes, but it requires physical skill to use effectively.) By making these things techniques and not spells, they cannot be poached by other classes (similar to Channel Divinity), and they don't have to do a bunch of convoluted design to make them play nice with other spellcasting options.
*This is pure spitballing and would require plenty of testing. Please don't let "actually that specific design is horrible flaming rotten garbage" criticisms bleed into the more fundamental point of a class that requires both supernatural power and physical/material/mundane skill to be effective.