Not having carried out a proper scientific investigation in the kitchen, I can’s safe for sure, but I would doubt it makes a difference. Let’s delve into a little onion chemistry which will of necessity involve some chemical terminology that hopefully will not make you cry. Remember that you cannot make any judgements about a chemical based on the complexity of its name.
Onions do not relish becoming food for microbes, insects, rodents or indeed, people. Unable to run away from such predators, they have evolved an ability to protect themselves through unleashing some impressive chemical weaponry. So here we go with the chemical names. Onions contain odourless S-alk(en)yl cysteine S-oxides that are the precursors to the nasty deterrent, (Z)-propanthial S-oxide. This is the “lachrimatory factor” that irritates the eye, stimulating an attempt to wash it away with tears.
The mechanism by which this compound is produced has been thoroughly investigated. When the tissues of the onion are disturbed, an enzyme, alliinase is released and causes the breakdown of the alk(en)yl cysteine S-oxides into (E)-1-propenesulfenic acid that under the influence of another enzyme, lachrimatory factor synthase (LFS) is converted to the offensive (Z)-propanthial S-oxide, the “lacrimatory factor.” That term derives from the ancient Greek for “tear.”
Now for the battle against the lachrimatory factor. Since this is highly volatile, and volatility is a function of temperature, chopping a refrigerated onion will reduce the onslaught on the eyes. So will the use of a very sharp knife since this will result in less tissue destruction and therefore reduced release of alliinase. As for coating the knife with olive oil, there are two theoretical possibilities. A lubricated knife may slice more smoothly through the onion and some of the irritating compound may dissolve in the olive oil before it evaporates. Both of these are unlikely to make an impact. If really bothered, you can always purchase special onion goggles that form a tight seal around the eyes and prevent any contact with the lachrimatory factor.
There is another way that tears can be avoided. Through genetic engineering techniques, the gene that codes for lachrimatory factor synthase in the onion can be silenced. But that then raises the issue of genetic modification and some cooks would likely rather cry than chop GM onions.