If it's just "Mecha Frieza but twice as strong", Vegeta stomps. If it's "Mecha Frieza but he can use the Kaio-Ken as far as his body will take him", Frieza wins, but it's not a one-shot.
Obviously the OP's referring to Freezamite Freeza, who stomps without Kaioken due to being MSSJ tier.
Seriously though, we'll probably need some more clarification on the scenario. Is it limited to Kaioken x2? Is this a hypothetical pre-Rosat Grade 2 Vegeta? Lot of things need to be confirmed so that this is more than just Vegeta oneshotting Freezie Pop.