Can a 10% resistor be used as a 1% resistor?
You don't provide much info regarding the environment that the circuit will be used in or the specific resistor types.
If you expect temperature variations (or even temperature change caused by self heating) then temperature coefficient becomes important and the initial measured resistance value may be soon way off.

By 10% you probably refer to either carbon or carbon film resistor types.

Carbon resistors typically have a have a temperature coefficient of 5000 ppm/°C which means 0.5%. That is 5% value change with just 10°C variation.

Carbon film resistors have temperature coefficients typically around 200 to 500ppm/°C, which can give a value variation of 0.2% to 0.5% per 10°C temperature variation.

On the other hand a metal film resistor (which is probably what you refer to by 1% tolerance) has a temperature coefficients ranging between 10 and 100 ppm/°C, so a variation of 10°C will result in a value change of just 0.01% to 0.1%