Current sources are not entirely independent of load changes, by the way! So switching the shunt can really cause the generation of a differing current.
....
Don't expect the current source to be absolutely precise, the most are not.
Don't expect the current source to be absolutely precise
Don't expect your A/D to be absolutely precise
Don't expect your DMM to be absolutely precise

DO NOT CONFUSE RESOLUTION WITH PRECISION

The only way you will get ANY precision is by constantly comparing to a precision resistor
If you want your 5% resistor to be within .11% you must use a .01% reference resistor.

Erik

PS In My opinion you are on a fools errand, a lower precision resistor will drift way more than a high precision resistor with temperature/age/humidity/current/.... so if you need the .1% precision for any length of time and any change in conditions you will never make it with a 'calibrated' resistor.
HOWEVER, there is one case where your scheme might work: if you do not need precision, but matching (as in differential analog) some have gotten by with matching IDENTICAL (brand/type/etc)resistors.

For those that like to misunderstand in order to get an opportunity to bitch:
talking about a 'fools errand' is NOT calling the OP a fool, if in doubt, look it up.