Davidson suffered a serious knee injury in the first leg in Armenia and is expected to be out for around three months.
It is a blow for Saints, who have to overturn a 1-0 deficit from the first leg, but Graham Cummins (hip) has trained all week and Chris Millar (hamstring) will be assessed after the pair missed the first leg of the first qualifying round tie.
Steven Anderson could feature after playing 60 minutes of a friendly on Saturday, while fellow defender Frazer Wright is also in contention, but Dave Mackay (hip) remains out following surgery.
St Johnstone manager Tommy Wright says he is expecting a “totally different game” when his side welcome Alashkert to Perth after having to contend with temperatures approaching 40C in the first tie.
Wright feels the change in conditions and a better understanding of their opponents on Thursday can help his side reach the second qualifying round.
He said: “We didn’t pass the ball well and we know that but the conditions didn’t allow us to press when we really could have. I think it affected concentration and decision-making. That’s not an excuse, we should have dealt with it better.
“At home, they will have to experience all we had to experience in terms of travel, being in a hotel, and the temperature will allow us to play with a better intensity, particularly when they have the ball. I’m expecting a totally different game.
“I think the key thing will be the fact that we have seen them and played against them. The importance of that can’t be underestimated. The lads will have a better understanding.
“I’d imagine we will get seven, eight or nine thousand as well so it’s going to be a pretty good atmosphere as well and I don’t know if they have experienced that recently.”
Midfielder David Wotherspoon added: “We are excited for the game. We need to prove a point after getting beat 1-0 away from home and show that we are a good side in Europe and can progress to the next round.
“We under-performed over there and I think, with a good performance, we can get through to the next round.
“We didn’t know much about them going into the game apart from a few clips, but they showed they are a decent side. They kept the ball well, they were very sharp. They moved the ball well and created chances.
“I think if we perform to our game, we can beat them. If we pressure them high up the park and play at a high intensity, I think we can cause them problems.”
Saints face a trip to Kazakhstan if they progress after Kairat Almaty beat Red Star Belgrade 2-1 in their second leg for a 4-1 aggregate success.