It was revealed during the week that the Ayrshire club reached agreement with a creditor over an unpaid sum of £16,000 to avoid the threat of a winding-up order.
Financial fears resonate with Smith who has come through turbulent times himself at Dundee, experiencing administration as a player in 2003 and replacing Gordon Chisholm as boss when the club were plunged into administration again in October 2010.
The former Celtic defender believes the match will allow Kilmarnock players to forget any concerns they may be harbouring.
He said: "It is a bit unnerving when you see that things aren't getting paid. Obviously their thoughts might be elsewhere.
"I know that players tend to focus just on the football but things off the park can affect the way they are thinking going into the game.
"But what tends to happen is that when you go on to the park you forget about everything else and you concentrate fully on the game. It is a release."
Smith is looking to replenish his squad before the transfer window closes and has not given up on his bid to bring Gary Harkins back to Dens Park on loan and hopes one or two more can be added before the transfer window closes.
Despite the threat of relegation for the SPL's bottom side, he says Dundee are still a "great club to play football for".
He said: The bonus is that we are in the SPL.
"I think players should want to come here to a club that is run properly now, given all the problems we have had in the past.
"It is a tight ship now, we are living within our means and that is the way forward for us.
"We want to bring guys in who are hungry to do well here and to make sure that we stay in this league, players who bring in quality but who also have that fight and desire to do well for Dundee."