"insignificant role" is correct and usable in written English.
It is often used to indicate that someone or something has a role that does not hold much importance. For example, "The volunteers in the play had an insignificant role, but they were still essential for the production to be successful."
"Football played an insignificant role in the 1914 truce," he tweeted recently.
"She has been the leading voice in Europe and played a not insignificant role in questions of global finance.
Despite al-Qaida's presence in the FATA, he continued, it plays a surprisingly insignificant role in Afghanistan, where the numbers of foreign fighters remain relatively low.
Several of them believed that it should be a junior official whose rank would be commensurate with his almost laughably insignificant role.
It was once fortified, with its own castello, and played a not insignificant role in the wars between Florence & her hated rival Siena.
Much of the pressure for the stimulus package came from the LDP's junior coalition partner, New Komeito, a Buddhist-affiliated party which hitherto has played an insignificant role.
Before 1988, soft money played an insignificant role, though it was permitted by a loophole in the post-Watergate federal election laws passed in 1974, which allowed unrestricted donations to political parties for party-building activities, like voter registration drives.
Like a waterborne Tiger Woods, Yelas is under constant pressure to perform -- and to do so in an enterprise in which plain old scratch-your-head luck has been said to play a not insignificant role.
Michael's, which has a sister restaurant in midtown Manhattan, played a not insignificant role in bringing California cuisine to the attention of the rest of the country more than 20 years ago.
In contrast to TPU material, adhesive wear plays insignificant role for PTFE/bronze system.
The observation indicates that surface adsorption of the model pollutant plays insignificant role in the photodegradation.
