One almost expected a tie to be flung at Trap's old buddy Zbigniew Boniek when the Pole plucked the kindest draw imaginable from the pot.
It remains to be seen whether the FAI chief executive John Delaney's inadvertently broadcast gleeful guffaws on live television may yet come back to haunt this Irish team.
Estonia are the easiest draw; then again, as Richard Dunne more diplomatically averred, all four Pot 2 inhabitants would have been crossing fingers in anticipation of Ireland.
Tallinn provided a pit stop -- quite an entertaining one at that -- en route to Ireland's last major championship appointment a decade ago. Prohibitive odds, generally 4/9, hint that this jewel of a city will do so once more.
Former Ireland manager Brian Kerr has more recent knowledge of how to trump the Estonians; his Faroe Islands minnows did just that at the inhospitable Toftir ground in their Group C qualifier just four months ago.
While Kerr deserves much of the kudos for a result that leapfrogged the Faroese momentarily above Wales in the world rankings, the Estonians clearly didn't fancy the poor conditions. After all, even Barcelona would struggle to get a grip on the wildest day Fanad United could have delivered in their Tragh-a-Lough ground in days of yore.
"We were in control for large parts of the game because they were down to 10 men after 25 minutes," recalls Kerr, still undecided on whether to re-commit to the Faroe Islands as they prepare to lock horns with Ireland in 2014 World Cup qualifying.
"It was unusual for us to have so much possession but, funnily enough, myself and my assistant Johnny McDonnell had worked in training on how we would use possession. Normally we play fairly constantly on the retreat, but we were controlled.
"Our young, 41-year-old goalkeeper, Jakup Mikkelsen, was brilliant when he really had to be. We got a break for the penalty before half-time. We scored that and we were away."
The Estonians were the beneficiaries of Serbia's hooliganism problems which resulted in the game between Italy and Serbia in Genoa being awarded 3-0 to the Italians; despite winning three away matches, including one in Belgrade, the former Soviet state finished 10 points adrift of group winners Italy.
The Faroes should arguably have completed the double against Estonia, instead conceding two injury-time goals in Tallinn in the group's opening encounter, Kerr's "worst result in football, ever".
"They're the only team to have lost against the bottom-seeded team in any of the qualification groups," continues Kerr. "Maybe we should have qualified for the play-offs on a head-to-head because we had the better results against them!
"Seriously though, Ireland should have too much for Estonia, the fourth best team in the group who have managed to reach the play-offs by catching other teams on the hop.
"Estonia are a well-organised group, an effective unit, but they don't have great players, so you'd think that Ireland would have a little too much quality for them, even if Giovanni Trapattoni might be missing a few players.
"I thought they were a decent team when we analysed them, fairly even-mannered in style, but I didn't expect them to finish ahead of two of the teams who were at the last World Cup, or even for that matter Northern Ireland, whom they beat twice."
Estonia generally play a straight-forward 4-4-2, albeit they flirt with 4-2-3-1, a system which would normally threaten Ireland's sterile 4-4-2 and Trapattoni's preference for an orthodox striking duo, although such concerns are mitigated by Estonia's lack of quality.
The team's strikers -- Jarmo Ahjupera, Tarmo Kink, Kaimar Saag and Sergei Zenjov -- boast 117 international caps between them but have scored only 10 goals in total and they have struggled at home, winning just two games in Tallinn during the qualification phase.
Konstantin Vassiljev is the sole Estonian who can qualify for star status, yet he, like his team-mates, plays with an unglamorous European side, in his case Russian outfit Amka Perm. It was his double that put paid to the North in Belfast last week.
Kink, who can operate on the right or left, plies his trade with Middlesbrough, albeit in the reserves, and it was his long-range strike that set his side on the way to the definitive victory over Serbia in Belgrade after being 1-0 down, while Saag, who plays with Silkeborg IF in Denmark, operates in the little-and-large partnership alongside rangy FC Karpaty Lviv striker Zenjov.
"There's really no comparison between the sides because most of Ireland's players are in the Premier League, while Estonians are scattered around Europe," says Kerr.
"They do have a very good spirit, though, and as I know to my cost they are well capable of scoring late goals. And they can be a potent attacking unit because they scored three goals in Belgrade and four when beating Northern Ireland.
"So, they have a bit about them, but overall I wouldn't expect them to pose that much difficulty to the Irish side. Ireland have been playing very well away from home, they're unbeaten in qualification (away) and capable of keeping it tight in defence.
"Even without Kevin Doyle and perhaps Robbie Keane, we should have enough striking options to deal with Estonia, whereas they would struggle, I feel, should they lose any of their key players."
Estonia FA president Aivar Pohlak greeted the draw with the words: "this is what we want." However, form suggests that his side should not be capable of wiping the broad smiles from Irish faces.