So, I notice that I have no Electric-type attacks on this team, and I think that's a problem. Would Azelf or Gardevoir be a good replacement for Alakazam? If so, what are the best movesets?
Azelf would be better offensively.
A Mixed Choice Scarf set could work:
Azelf @ Choice Scarf
Naive Nature
EVs: 4 Atk / 252 Sp. Atk / 252 Spe
~ Explosion ~
~ Thunderbolt ~
~ Flamethrower / Fire Blast ~
~ Psychic ~
This might actually work better than Alakazam. Azelf still outspeeds Timid Choice Scarf Gengar and the Dragon Dancers after a single Dragon Dance. Anyway, Psychic is STABed but use it cautiously as Scizor, Tyranitar and Weavile will all happily switch in on it and take out Azelf with Pursuit. Flamethrower / Fire Blast covers Scizor and you can actually use it to turn the tables on a Choiced Scizor stuck on anything not named Bullet Punch. Fire Blast's accuracy can be a letdown but its still more than useable. Thunderbolt covers Gyarados and Azelf will easily outspeed it even after Gyarados has a Dragon Dance behind it. Explosion is used for dealing with Blissey and Snorlax as Trick would. Even with little Attack investment, it is still enough to take them out. If the loss of power is a concern, you can run a Rash Nature with the same EV spread since Azelf will still outspeed any Dragon Dancer after they have a Dragon Dance behind them but then you are outsped by Timid Choice Scarf Gengar and he will happily Shadow Ball Azelf. Against Tyranitar and Scizor, you will have to be careful of them since they pose a threat to this set. Tyranitar will have to be really weakened and Scizor will have to be Choiced and stuck on anything other than Bullet Punch for you to deal with them.
Azelf can run an all Physical version of this set with Zen Headbutt in place of Psychic, Ice Punch or Fire Punch in place of Flamethrower (Ice Punch is better in my experience since it murders Mence easily), and U-Turn, Trick or ThunderPunch in the Thunderbolt slot. Use an Adamant or Jolly Nature if going down that route with a spread of 4 HP / 252 Atk / 252 Spe.
An all Special version is essentially the above set with Trick or U-Turn over Explosion. Use a Modest or Timid Nature for that set with 4 HP / 252 Sp. Atk / 252 Spe.
Gardevoir could pull off a similar set but Azelf is a much better revenge killer in OU. Gardevoir at best can only outrun Adamant Gyarados after a Dragon Dance assuming Gardevoir is Timid and Jolly Weavile with a Modest Nature. Gardevoir however is studier on the Special side but that is really all it has over Azelf. Azelf is sturdier on the Physical side (lol) barring Tracing Intimidate from Gyarados or Salamence, has a higher base Special Attack and Speed and a much better base Attack so it can viably run a Mixed Scarf set.
Another option worth consideration is Grass Knot. It will give Azelf something to hit Tyranitar with but it will only be a 2HKO on 252 HP / 0 Sp. Def versions after Stealth Rock if running a Naive or Timid Nature but by using a Rash or Modest Nature, you have a higher chance of achieving it without Stealth Rock. Hidden Power [Fighting] can be used too although it is still a 2HKO after Stealth Rock with a Timid or Naive Nature but you'll always 2HKO it if using a Modest or Rash Nature. Just watch out for Specially Defensive variants.