Occasion (While Doing / On The Occasion Of)

Referring to an occasion in ordinary formal writing: a manual, a procedure, an email.

～際に vs ～にあたり: Use 際に. It is the neutral marker for 'when X happens' and carries no ceremony. にあたり marks the threshold of an undertaking (開会にあたり一言), which is what you want at a podium and far too grand for an instruction.

Referring to a future occasion when you might meet again.

～折には vs ～に際して: 折には is the softer, more personal of the two and suits set courtesies (お近くにお越しの折には). に際して is institutional, attached to events and procedures, so it sounds cold in a pleasantry.

Doing a second thing while you are out doing the first.

Noun がてら vs Noun かたがた: がてら is the more everyday of the two and takes concrete errands (散歩がてら買い物). かたがた is stiffer and takes formal purposes, especially courtesies (ご挨拶かたがた伺います), so it is what you write in a letter rather than what you say about a walk.