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I decided to finally write this myself! Posting here as an answer for anyone that is interested. I decided to use the built-in SemistandardSkewTableaux class instead of the SkewTableaux class as it seems that the latter does not have a ''.list()'' method. It would also be easy to modify this code to make it work on more general skew SSYT.

def des(T):
    out = []
    for i in range(1,T.size()):
        if T.cells_containing(i)[0][0]<T.cells_containing(i+1)[0][0]:
            out += [i]
    return out

def maj(T):
    return sum(des(T))

def majpol(lmbda,mu):
    var('q')
    out = 0
    for T in SemistandardSkewTableaux([lmbda,mu],[1]*(sum(lmbda)-sum(mu))):
        out += q**maj(T)
    return out

So one can write for example

lmbda = [3,2]
mu = [1]
majpol(lmbda,mu)

which outputs

q^4 + q^3 + 2*q^2 + q