McGeechan's men have picked up just one win from six games and are hoping for a change of luck as they travel to Newport Gwent Dragons in the Anglo-Welsh competition on Saturday night.
Wasps bring England's Tom Rees straight back into their side following his return from World Cup duty in the only change to the side edged out 26-25 at Harlequins last week.
Director of rugby McGeechan said: "The EDF Energy Cup presents a different challenge to the domestic league, and for us it's good to embark on a new competition.
"It's our first cross-border encounter of the season and valuable experience for the players - they know how important it is to perform well.
"It's great to have Tom Rees back out on the domestic stage and we look forward to facing our opposition, Newport Gwent Dragons, who are going well in the Magners League.
"Playing in Wales is always a challenge and we know that we will have to be on top of our game to come away with a win."
The Dragons, fourth in the Magners League, go into the Rodney Parade encounter in good heart having won their last two matches against Leinster and Edinburgh.
The visit of Wasps is something the Welsh side are relishing, even though flanker Richard Parks is expecting a highly-physical encounter.
Parks said: "As a squad, we have been pleased with our recent performances in the Magners League, which has prepared us for the intensity of the cup competitions we have coming up.
"We are expecting a physical onslaught from Wasps and the game will be a real battle up front.
"They may not have started their season well but they have that knack of doing well in cup competitions and we will have to play to our strengths if we are to start with a win."
Parks, signed from Perpignan in the summer, added: "On a personal note, I am enjoying my time at the Dragons and have settled in well.
"We are aiming to do well in the up-and-coming cup competitions and are getting fired up for them."