The draws were made for the early rounds of the competition last week with the 13 Championship sides based in England joined by three League 1 clubs in the draw.
Batley will face Halifax Panthers in an all-Yorkshire affair while Dewsbury will travel to Whitehaven. Both games are to be played on March 21.
The early rounds of the competition will double up as 1895 Cup qualifiers, with the four teams who get through the first two rounds, earning their place in the semi-finals. The final of the 1895 Cup will be played at Wembley on the same day as the Challenge Cup final.
The four Championship or League 1 sides who get through the opening two rounds will also join the 12 Super League clubs in round three of the Challenge Cup, giving both the Rams and Bulldogs two chances to reach Wembley.
“These games are doubling up as the 1895 Cup so if you win your two games you are already in the semi-final of the 1895 Cup,” said Bulldogs head coach Craig Lingard.
“You are effectively three games away from Wembley and as a Championship or League 1 club when can you ever say that.
“If we get through the first and second round that means there are some tough teams who won’t be in the semi-final, so there is certainly incentive there for us to try and win these two games.”
If Batley can beat Halifax, they will face the winners of the tie between Featherstone Rovers and Bradford Bulls.
Dewsbury will play the victors of the clash between West Wales Raiders and Widnes Vikings, if they triumph in Cumbria.
Rams chief Lee Greenwood believes there could be some shock results in the Cup, given the amount of time teams outside of Super League have been out of action.
He said: “If I were to pick an ideal draw, that might not have been it but we are happy to be back playing and have some fixtures to look forward to.
“Previous form is going to be out the window. Everyone will have gone about things differently in their pre-seasons.
“It has been so long since people have played as well, in these early rounds of the Cup and the league, anything could happen. Expect the unexpected in these early rounds.
“In the first few rounds of the season we will see some unexpected results. We know what it will be like going up to Whitehaven, sat with our face masks on and socially distanced on a bus. That is not ideal.
“We went up there last year in very tricky conditions on a Wednesday night after playing on a Sunday and we managed to get into the next round. That is what we will hope to do this time.”