The fourth-round tie at the Bet Butler Stadium, which was due to take place tomorrow, has been postponed after freezing temperatures left the pitch solid.
Accies will now make the trip to the Rock on Tuesday as the Irn-Bru First Division rivals bid for a place in the last 16 of the competition.
Reid has changed his side's style in recent weeks and was rewarded with 1-0 wins over Morton and Partick Thistle and then saw his side come agonisingly close to clinching a hat-trick of triumphs at Falkirk last Saturday.
Reid said: "We have to take stock of where we are and it is horses for courses. We go to Dumbarton, we have already been down there and drawn 3-3.
"We have to make sure with our formation that we are hard to beat but also a threat going forward.
"Let's be honest, in the three games we have not had enough of a threat going forward.
"But we are hard to beat and we had to make ourselves that way because we were too soft-centred.
"The fans were delighted with the Morton and Thistle games when we won that way and we were eight minutes away from them being delighted again.
"We will take what is thrown at us. We are a young group and we are developing all the time. There are positive signs."