Solvents for tartrates / tannins that won't attack glass
The CRC Handbook indicates that potassium d-tartrate and dl-tartrate are soluble to the extent of 100-150 grams per 100 mL H2O vs about 0.5 grams for the bitartrate. Rather than using acid to clean the decanter, alkali would neutralize the bitartrate to the much more soluble tartrate . Washing soda (Na2CO3) should not be too alkaline, but even sodium bicarbonate (NaHCO3) might work. Neither is expected to be harmful at the level that might exist after rinsing.

The tannins or other organic might slow things down. Bleach (NaClO) is alkaline, and although bleach is toxic if ingested, it should present no problem if the decanter is rinsed. Water could be flushed around inside the decanter, then tested with litmus paper. Or the decanter could be rinsed with vinegar and a little honey to remove the bleach: the vinegar makes the liquid acidic (HClO) and the honey gets oxidized to gluconic acid, consuming all the bleach - leaving a sweet, tart taste.