The decision regarding the annual Tyrone Volunteers Commemoration comes after opposition to next Sunday's event.
This year it falls on the 40th anniversary of the deaths of two IRA men from Castlederg, Seamus Harvey and Gerard McGlynn, who died in 1973 when the car bomb they were transporting detonated early.
Delegations from both Sinn Féin and the DUP met with the Parades Commission on Tuesday over the issue.
Sinn Féin said the development is an attempt to "defuse the contentious scenario".
Councillor Ruairi McHugh added: "This parade is organised to show respect for those who gave their lives for this community. It should never have been an issue of controversy- it has been 'made' controversial by unionist politicians.
"Our initiative will consist of choosing to go along John Street which avoids passing the cenotaph and the Methodist church.
"We have proposed this initiative to take the controversy out of it while reducing tension. On the back of this initiative, we wish to engage with all key stakeholders in relation to the issue of the town centre being designated as a shared space for all traditions, in this mainly nationalist town."
Speaking after the meeting with the Parades Commission, Arlene Foster of the DUP said the event should be cancelled altogether.
"There is a wider issue being raised regarding the glorification of a proscribed organisation and how the police investigate such a matter," the Fermanagh and South Tyrone MLA said.
"I have asked for a meeting with the Chief Constable regarding this wider issue which effects pro-PIRA events held all over NI. It would seem that under the Terrorism Act the police has grounds to investigate and bring prosecutions for the promotion of a proscribed organisation."
DUP West Tyrone MLA Thomas Buchanan added: "Whilst the Parades Commission does not have the power to ban a parade, we informed them that we utterly reject that such a parade should even take place regardless of the route. It should be cancelled."
He called for Sinn Féin MLA Gerry Kelly, who is the keynote speaker at the event, to "recognise its offensive nature" and withdraw from the "provocative event".
Castlederg UUP councillor Derek Hussey also called for the parade to be banned.
He continued: "If Commissioners are not in a position to do so they should refer the issue to the Chief Constable and Secretary of State immediately as there is no doubt that they retain such powers."