I am also trying to sequence a 135 bp PCR product. Gel purification
worked fine, but it's too expensive and labour-intensive. I talked to
Qiagen (no affiliation on this side) on the phone and they said they had
columns capable of 100 % separating my product from my 20mer primers.
They were also so kind to provide me with some sample columns for
testing. However, I didn't get to do the testing yet, so I can't
definitely say if it actually works or not.
Why not give them a call and ask for samples?