It is impossible to guarantee that a tax return will not be audited by the IRS.
The IRS audits approximately 4 out of 1000 returns per year, according to recent data. While that is a low rate, there is never any guarantee that the IRS will not audit a tax return regardless of the taxpayer situation as some returns are drawn randomly for audit.
As you mentioned, there isn't anywhere to indicate the $3000 catch-up contribution on the tax return as the IRS has no reporting requirements for this. As such, you can feel confident that your return is conforming to the tax law in this regard.
Most IRS audits involve sending a letter where they may require more information. In your case, the extra $3000 of contributions does conform to the tax law. This link from the IRS has good information on the 403(b) catch-up contributions: IRS 403(b) catch-up contributions.
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