Teicníocht is given in Ó Dónaill but not teicníc.
Teicníc is in EID and NEID.
Don't see why "modh oibre" couldn't be used instead of gaelicising an English word.
The tearma.ie entry for “technique” shows that they represent two different meanings; teicníocht is a practical aspect (e.g. the technique of using Chladni patterns in violin construction), and teicníc is practical ability (e.g. the technique of Jascha Heifetz in violin playing).
NB: "technique" is Greek, via French; in English it's a borrowing, too, as most science/tech words tend to be in all languages.