Except for the 1953 RLDS edition, all the (extant) textual sources here read whither; the 1953 edition reads whether, an impossible reading. We undoubtedly have a typo in this instance. The critical text will maintain the original, correct whither. For a list of other cases in the history of the text where whither and whether have been mixed up, see under 1 Nephi 22:4. One should also note here that whither is used even though no motion is involved. For further discussion of this usage for whither, see under Mormon 8:10.
Here in the printer’s manuscript, Oliver Cowdery initially wrote which instead of whither (“or upon the place which he would keep it”). Virtually immediately Oliver crossed out the which and supralinearly inserted the correct whither (there is no change in the level of ink flow for the correction). He appears to have simply misread the whither in 𝓞 as which. Oliver didn’t make this kind of mix-up anywhere else in his manuscript work.
Summary: Maintain in Ether 14:1 the use of whither, the reading of the earliest text (“or upon the place whither he would keep it”).