Idiom to say "with lowest impact"

Although this doesn't zero in on the question, the idiom below might be of some use to you

On one's radar screen

In one's conscious awareness as a possibility or as an existing phenomenon:

The governor said that running for president was not even on her radar screen.

So, you could perhaps say that the other processes are not on/are out of your radar screen.

EDIT: Thanks to Jim, who brought to my attention that On one's radar screen doesn't quite fit the bill. As such, I suggest

In the cross hairs

being aimed at by a gun (such as a rifle) that has an aiming device with crosshairs —often used figuratively

The senator's voting record was in the crosshairs of his political rivals.

OP might thus say:

The dependent processes are not in the crosshairs of the process change.

Another way of saying this is:

The dependent processes shall remain outside the purview of the process change.

Merriam-Webster defines purview thus:

The limit, purpose, or scope of a statute

the range or limit of authority, competence, responsibility, concern, or intention.

You don't need any fancy language.

Borrowing from two of your sentences I suggest

We are doing our best to make sure this change has the least possible impact on other processes.

• We are looking for / believe we have come up with a magic bullet.

magic bullet [compound] noun

something that cures or remedies without causing harmful side effects:

• So far there is no magic bullet for economic woes.

[Dictionary.com]