Downgrade the Conflict.
Of all the characteristic grunge elements, two stand out as core looks: Plaid flannel button-downs and black leather combat boots, often the classic Dr. Marten-style. We'll get to the plaid in a moment.
Combat boots, 1992: Flat, clunky, rubber-bottomed lace-ups that hit at roughly mid-calf
These were cool, and they went with everything. They contrasted with the girly floral dress and made ugly a fashion statement. They offered a modicum of protection in the mosh pit. They upped the "Who cares?" ante through sheer force of clunk.
Combat boots, then, may not fit your current, presumably more-refined style. To hint at combat without weighing down your look, keep the black and the laces, and tone down the ugly.
Combat boots, revised: Black leather lace-up or buckle-clad boots, mid-calf, with either a flatform or a wedge platform sole.
Now, fashionably heavy-shoed, leather-clad, cinched and well-torn, we come to the grunge pièce de résistance, the uniform, the shirt heard 'round the world ...