Ok,
There is a scales of war background called, "gritty sergeant" that gives you proficiency with one military weapon of your choice. That gives you longsword proficiency.
Then you can take swordmage multiclass feat to use it with all your implement attacks.
Take intelligent blademaster (swordmage feat) instead of melee training (intelligence) so you don't lose out on damage on your basic attacks.
That's just two feats instead of three, and swordmage multiclass is an excellent feat that you'd probably want to take anyway.
If you just want it for implement attacks, you just need one feat: arcane implement proficiency. You don't need to be proficient in an implement as a weapon to use it simply as a weapon.