Perhaps something like the following (provisionally), a Basal Technique (something you can take at an early level.)
Grasp of the Storm
Range: 30'
Target: One creature
Action: Attack (can replace one attack in the Attack action)
Combat: Make a spell attack against a creature you can see within range. On a hit, deal your weapon's damage as lightning damage, and pull the target adjacent to you. You have advantage on this attack roll if the target is unable to move under its own power. If the target is physically fixed in place and cannot move, it instead takes an additional 1d8 bashing damage, and does not move.
Utility: Outside of combat, you may use this technique to pull willing creatures or objects across gaps or hazards, and with enough skill, do so without any harm done to them. Instead of an attack roll, make an Arcana check against a DC equal to the target's weight in pounds divided by 10 (minimum 5.) On a successs, the target is pulled up to 30 feet to a space adjacent to you. If the roll fails by less than 5 points, you still pull the target to you, but it takes lightning damage equal to your weapon damage. If the roll fails by 5 or more, the target does not move but also does not take damage, and is immune to this technique for one hour due to static electric buildup.
This provides niche but useful utility outside of combat, while still capturing the core essence of the effect. It notably does not use a saving throw; hitting with the attack is enough. Dealing weapon damage as lightning damage also means that a Swordmage with beefier weapons has scarier attacks, which seems reasonable to me.