Sorry - it's appears I've solved my own query! I checked some newspaper databases shortly after posting and found evidence that seems to confirm the regiment was issued with grenadier caps in accordance with their new title.
I've attached transcripts of the newspaper articles below for the interest of Napoleon Series members -

The Morning Post, December 27, 1815 - references "new shaped grenadiers cap"
"Monday being Christmas Day, was the day appointed for the first inspection of the 1st Regiment of Foot Guards, since it has been appointed, by special and Royal command, a Grenadier Regiment, to be called the 1st Regiment of Grenadier Guards.
The 1st Battalion appeared on the Parade in St. James's Park early in the morning, in their new clothing and caps. They were accompanied by the bands of the Coldstream and the 3d Regiment of Foot Guards, their own band being in France, headed by the two head drum-majors in their state uniforms. A little before ten the Archduke John arrived, conducted by Col. Cooke, one of the Commander-in-Chief's Aid[e]-de-Camps. His Imperial Highness was received by Sir H. Torrens, the Officers about to mount guard, and other distinguished officers. The Duke of York being Colonel of the Regiment, arrived at York House a few minutes before ten o'clock from Oatlands, for the purpose of inspecting them, when after His Royal Highness had dressed in the regimentals of the Regiment, with the new shaped grenadiers cap, he walked to the parade, accompanied by Lord F. Bentinck, the Lieutenant-Colonel of the Regiment. His Royal Highness was received with all due military honours; His Royal Highness then proceeded to inspect the Guards. The colours were afterwards trooped, and the new colours brought out from the Orderly Room, and presented to them, which have the addition of Waterloo inscribed on them, in addition to Corunna and Lincellis [sic]."

Morning Post, May 30, 1816 - Prince Regent's Levee at Carlton House
"A Guard of Honour of the Grenadier Guards, under the command of Colonel Joddrell, with the Band in their state uniform, with caps to correspond with the Grenadiers, which they have within these few days had given to them…"