python shuffling with a parameter to get the same result

As the documentation explains:

The functions supplied by this module are actually bound methods of a hidden instance of the random.Random class. You can instantiate your own instances of Random to get generators that don’t share state.

So, you can just create your own random.Random instance, with its own seed, which will not affect the global functions at all:

>>> import random
>>> x = [1, 2, 3, 4, 5, 6]
>>> random.Random(4).shuffle(x)
>>> x
[4, 6, 5, 1, 3, 2]
>>> x = [1, 2, 3, 4, 5, 6]
>>> random.Random(4).shuffle(x)
>>> x
[4, 6, 5, 1, 3, 2]

(You can also keep around the Random instance and re-seed it instead of creating new ones over and over; there’s not too much difference.)