I frankly think that Jean had the most appropriate question:
I happen to live in a rather humid climate here in Hawaii, a literal stone's-throw away from the Pacific Ocean, so oiling my blades every quarter is less an option than a necessity, although I keep my blades in shirasaya inside a traditional katanadansu. Speaking as a Petroleum Engineer, unless you choose to use a denatured alcohol (usually isopropanol) or a ketone (acetone), you're simply not going to remove all of the old oil previously applied to your blade. And there is really no reason to remove it all; what you're trying to do is to keep the "old" oil from polymerizing (getting gummy) due to heat, or maybe some residue inside the saya. The thin new coat of oil is intended to provide a passivation (oxygen-resistant) layer to preclude rust. Done correctly, there won't be a build-up of oily residue in the saya.
There may also be times when uchiko is warranted, but I'm not addressing that; however, using uchiko just to remove previous applications of oil is really tremendous overkill, & that alone won't work, anyway.
Ken