You ask whether your proposed representation would be acceptable. Offhand, I would be cautious about infix notation for these negative operators.
A NOR B would be expressed as "neither A nor B".
A NAND B would be expressed as "not A and B". Often, intensifiers will also be prefixed to emphasise a NAND or NOR case and clarify the scope of the negative, such as "not both A and B", or "not any of A or B".
In both cases, the negative is introduced first in English, before the list of items, which accords more closely with the structure of the representations you are trying to replace -
NOT(A OR B) etc..
Even on a technical front, I'm not familiar with a programming language that has NOR or NAND infix operators.
If you must contract these expressions or use the name of the operator, I would suggest
Another problem is when there are more than two inputs. Unlike AND and OR, NAND and NOR are not associative, whereas "nor" in English has the same meaning and associative property as "or" (it's the introducing word "neither" which applies negation to the whole set, after they have been ORed together).
NOT(A OR B OR C) corresponds to the English "neither A nor B nor C" (i.e. none of the set is true), but that is not the same as
A NOR B NOR C (the meaning of which I can't mentally parse into English, and I'd have to sit down and write out a truth table to be sure).
Nand, of course, does not exist as an English word, but
A NAND B NAND C is equally different from "not A and B and C" in English (i.e. not all of the set is true) and from
NOT(A AND B AND C) formally.