The visit of the West Region champions will be a huge test for the Ants, with "Cotter" describing the clash as "a meeting of the rich and the poor".
However, he was upbeat as he looked forward to meeting the Ayrshire cracks, saying: "No doubt we'll be rated outright underdogs and not given a hope of getting through, but my players will not be fearful about going up against the Medda.
"Yes, they have every right to be cock-a-hoop after beating us 3-0 in a pre-season friendly, but we are a much-changed and improved side since, whereas it's arguable if you can say the same about them.
"My players will be up for the game and I'm sure the occasion will bring out the best in guys like Chris Mackie, so nobody should be considering this tie to be a foregone conclusion. We'll have nothing to lose and that makes us very dangerous opponents."
Benburb will entertain Saltcoats Vics, however a tough test awaits Glasgow southside big guns Pollok in having to head down to face Super Premier rivals Glenafton.
Another of Glasgow's hopefuls, Petershill, are delighted after landing the plum tie – an away game against reigning East Region champions and last season's beaten Emirates semi-finalists, Bonnyrigg Rose.
Peasy skipper Ryan Jordan admitted: "It's a toughie and I'm not going to pretend otherwise, but it's a good draw in the sense that playing the best is sure to bring out the best in ourselves.
"We've taken a tumble at home to so-called lesser lights Ballingry Rovers, Montrose Roselea and Cambuslang in recent years, so we're not overly unhappy about taking on one of the fancied East Region outfits in their own backyard.
"And it might work in our favour if Bonnyrigg beat Brechin in the big Scottish this week and earn a trip to St Mirren as it would be understandable if their players had their minds on that game more than ours."
Springburn co-gaffer Willie Patterson said: "Not one we'd have picked but, by the same token, I cannot imagine Bonnyrigg are doing cartwheels over landing ourselves.
"My only disappointment is over the tie being played a week on Saturday which is slightly unfair on us in terms of running the rule over Bonnyrigg as it can only happen this Saturday when they are up against Brechin City in their Cup replay rather than Junior opposition."
Draw: Steelend Vics v Arthurlie, Kirrie Thistle v Kilsyth, East Kilbride v Kinnoull, Deveronside v Glencairn, St Andrews Utd v Jeanfield Swifts, Newtongrange Star v Auchinleck Talbot, Musselburgh v Bellshill, Yoker v Forth, Hermes v Bo'ness, Culter v Edinburgh Utd, Ashfield v Ardeer, Dundee Violet v Dunipace or Livingston Utd, St Anthony's v Irvine Meadow, Linlithgow Rose v Fauldhouse, Glenafton v Pollok,
Pumpherston v Inverness City, Cumbernauld v Forfar West End, Camelon v Thorniewood, Beith v Sauchie, Montrose Roselea v Maryhill, Shettleston v Tayport, Dyce v Lochee Utd, Greenock v Shotts Bon Accord, Dundonald Bluebell v Oakley, Cumnock v Islavale, Johnstone Burgh v Buchanhaven Hearts, Bonnyrigg Rose v Petershill, Armadale Thistle v Rob Roy, Blackburn Utd v Blairgowrie, Rosyth v Brechin Vics, Kelty Hears v Penicuik, Benburb v Saltcoats. Ties on Saturday, November 17 at 1.45pm.