No, there is no practical way to remove an old bloodline. There are two ways to effectively remove a trait in theory:
1) The trait is an injury, and can be removed alongside any other injury.
2) The trait has an upgrade that is identical to the first one but in inverse, countering any effect you gained from the first one (+1 hp / -1 hp).
Neither method can be applied in practice to something like this. The second method is not applicable because we don't know which one the first is (could be any bloodline).
My suggestion: just keep the old bloodline on the unit. It's not going to dramatically upset the balance or immersion.