The 31-year-old former Town midfielder reckons his boyhood club look well-placed to spring a surprise on the top flight visitors in front of the watching nation this weekend.
The Welshman, from Pontesbury, is also relishing the prospect of his former Shrewsbury academy and senior team-mate Joe Hart returning to his hometown club.
Edwards is set to watch the third round Montgomery Waters Meadow tie on television and hopes Shrewsbury can heap similar misery on David Moyes as they did to his Everton side in 2003.
"I'd say it's a tie that West Ham fans wouldn't have liked," Reading man Edwards said.
"They're against an in-form, lower league team that, in front of the cameras, you know the will give their absolute all – like they have all season.
"West Ham will have to come here on the top of their game, have to put out a good team as well and it'll be a great cup tie for the neutral.
"There's definitely a lot of excitement around the club at the moment and I think the national media is starting to pick up on it.
"We've had some great cup ties here in recent years and Town have been on great cup runs. It's another to add to the list to hopefully reminisce about like Everton in 2003."
Edwards is a year older than Hart but the pair progressed through the ranks at Town together. The Wales international paid tribute to his former team-mate, who he insisted is a credit to the club.
"He was always set for a big future," Edwards added. "You could tell from when you first played against him at 14 or 15 that he would have a chance at being a professional – he was that composed as a goalkeeper.
"Through his teenage years he was very similar to what he is now. He hasn't changed, he's always been confident, but in a good way.
"He's always known that he's had good ability and used it in the right way, he works incredibly hard and I've been delighted to see him having such a wonderful career, starting at Shrewsbury.
"It's a great thing for the club to say there's an England goalie that earned so many caps and learned his trade here."