I'd advise you not to attempt Quarantine then, unless you have a seriously capable anemone quarantine system, as acclimating/maintaining Stichodactyla gigantea is difficult enough without the added stress created from an insufficient QT system !
Either cut away the rock or dip/brush it in a H2O2/RoDi solution ...
If you decide to attempt to persuade the S.g specimen to detach from the rock DO NOT use the ice cube "idiotism", its acutely stressful to the anemone and typically results only in shrinkage, not the desired movement ... It's purely bad advise, especially for the more difficult Stichodactyla gigantea/Heteractis magnifica species. Rather, add a "reasonably strong" pump to the acclimation chamber/container and make the anemone "uncomfortable" with the force of linear flow directed at its foot. Now, these species appreciate strong flow rates so its imperative to find a balance between "tissue tearing" and a "naturally brisk current" flow.
Do you have any prior experience with either of these species, honestly ? It should be stated you are undertaking a serious/difficult task with this species, the chance of transferring the "tomont" stage of ich is realistically low on the list of your concerns here ...