We have not been told who held these positions, so you could just make up new characters. However, if you want to use known names, there are a few things to consider.
For Senior Undersecretary to the Minister, the most logical candidate would have been Umbridge, since she is the only person known to have held that post. Unfortunately. this is impossible. Hogwarts Mystery made it clear that she was the head of the Improper Use of Magic Office during the 1980’s, and we know she worked her way up through that department, so in 1981 she definitely wasn’t the Senior Undersecretary.
That means we need someone else to fill this position. Considering the importance of the post it is likely that the occupant remained a person of importance during their Ministry career, becoming head of a Department or perhaps even Minister for Magic. Fudge himself would therefore be a logical choice. However, we know what job Fudge held during 1981, because he told us in PoA; he was Junior Minister in the Department of Magical Catastrophes. Another senior Ministry official, Barty Crouch Sr., also can’t have been Undersecretary in 1981, because he was Head of the Department of Magical Law Enforcement at the time.
That brings me to my two most likely choices. The first one is actually Crouch’s successor: Amelia Bones. The Department of Magical Law Enforcement is the largest and most powerful department in the Ministry, so it would be considered a promotion for the Senior Undersecretary to be appointed to that position. The most important counterargument I have to this choice is that I have trouble envisioning Amelia Bones working anywhere other than the Department of Magical Law Enforcement, because of her strong sense of justice, but that may just be my impression of her. Regardless, Amelia Bones seems like a solid choice.
My only other choice, funnily enough, is Amelia Bones’ successor: Pius Thicknesse. Like I said before, Head of the Department of Magical Law Enforcement is perhaps the most powerful position within the Ministry with the exception of Minister for Magic, so Thicknesse must have been important within the Ministry at that point. Furthermore, when Thicknesse became Minister after the coup, it doesn’t seem to have surprised many people (even though the policies he began implementing clearly did), which suggests that he had been a logical candidate to begin with. To me it seems that Thicknesse is a more natural choice for Undersecretary than Amelia Bones, although it does beg the question what position he held during Umbridge’s tenure in that role.
Now, let’s turn to your other question: who could have been Court Scribe in 1981. I must admit I had considered quite a few names before landing at the one I should have considered immediately, because she is the only person except for Percy who filled this position in the Main Series: Mafalda Hopkirk. You may recall that Hermione, while disguised as Mafalda, was immediately assumed by Umbridge as the help she requested to record-keep in the Muggle-born trials, which suggests she had experience in that role, possibly because she knew stenography. If you want to assign her the role of Court Scribe in 1981, you would only have to assume that this was a role she held at the start of her career, and that she subsequently made a transfer to the Improper Use of Magic Office. Court Scribe seems like a very junior role within the Ministry, so working in the Improper Use of Magic Office would likely have been a promotion. Being once more relegated to more menial tasks by the Death Eater led Ministry after the coup also seems to be on point for the Ministry at that point in time, as they had been undergoing an enormous transformation and needed skilled record-keepers for the now quite common court cases against Muggle-borns. And let’s face it, I rather doubt Mafalda would have had much choice in where she was put to work in a Ministry led by Death Eaters.
These are, of course, just suggestions. Like I said, if you want to create new characters for these positions, that is entirely up to you. But if you want to use known names, I think these would be suitable. I wish you good luck with your writing and if you have any more questions, feel free to ask.