I have an iPad Air with its camera. I need to show a color of my shoes to a person who will dye shoelaces for them. So I need to reliably capture and transfer this color somehow. I assume that simple photo is not enough because of monitor color profiles and calibration differences. I thought of using some "colorimeter" app for iPad and extracting a color hex code. Is it a feasible idea? What else can I do in my case without professional equipment?
iPads [in fact most mobile devices] tend to be a bit 'over contrasty' unless you actually calibrate the screen with a hardware colorimeter; which probably means that even on your own screen the colour will be wrong. It will also vary depending on backlight brightness & surrounding lighting conditions.
Sending that value to someone else, who also has a non-calibrated & potentially over-contrasty screen, in an uncontrolled backlight/ambient light environment, just multiplies the potential for error.
Your only real viable solution, so you both know you are seeing exactly the same thing would be to print varying samples of the colour until you can clearly see, in good light [cloudy daylight may be the closest you can both get to being the same value], that it is a true match... then post it, snail-mail.
Alternatively, both of you would need either professional Pantone swatches... or at a push, find a paint swatch at a local DIY shop, if you both can source the same paint manufacturer locally [or, again, post it].
Here's the important thing: "color" is a sensation that emerges in the mind, not a property of the physical universe.
We experience color when light hits the receptors in our eyes. We have different receptors which are more and less sensitive to different wavelengths, and the brain takes that information and a whole bunch of other context and the result is the sensation of color.
This is very different from the sense of smell, where there are some 10,000 different receptors in the nose, each directly linked to a particular molecule.
With vision, the perception of color is highly dependent on the environment. Consider this optical illusion:
The two dogs are actually exactly the same in terms of red-green-blue pixel values, but we perceive them as colored differently!
And that's not even considering other factors. The color of the light itself is a big deal, both in terms of white balance (see What is the meaning of "white balance"? and Does Auto White-Balance Really Work? How?) and spectrum covered (see How does the colour of ambient lighting affect colour rendition? and What white balance settings do I need to capture the cast of a coloured streetlight?).
Today's digital cameras use a reasonable (but far from perfect!) approximation of the data-gathering part of all of this, with photo-receptors with filters roughly like the sensitivity of the receptors in our eyes. And given an external reading (or manual input), they can adjust for white balance — and can even make a reasonable guess in many scenes. But they can't account for missing spectrum, and they just plain can't do any of the fancy processing that you are doing constantly every walking moment.
Beyond all that, different materials react differently to different lighting and to different angles of viewing. Color in print is inherently different from color on a screen, and even if we're considering reflected light, color on paper is different from color on, say, cloth. People often have the misconception that an RGB hexcode represents a true color in some way. But, really, it just can't.
Generally, even with our carefully calibrated camera profiles and monitors and workflows, what we hope for as photographers is to get a result which matches our artistic vision — being perfectly true to the human perception of the world (our literal vision) is out of reach. And that's when making prints or images for display on our own hardware. When making images which will be displayed on other people's computers or printed on other people's printers, all – bets – are – off.
All of this is why Pantone makes a lot of money on something which seems simple. They produce standards which can be used to reproduce similar-enough colors in a variety of media. So, one approach would be to get a Pantone sample which matches your shoes, and send the number of that. (And make sure you do the matching in similar lighting — daylight is going to be easiest, even though daylight too varies by location and time.) However, this is out of the budgetary reach of most individual humans. Another approach would be to find something else which matches the color closely and to send that.
To scan a precise color at home is nearly impossible or very expensive.
A practical solution would be to go to a professional printing shop with the shoes. They usually have paper samples of Pantone color and place your shoes next to the samples, which are the closest visually. So you know which color you want. Then send the Pantone color number to the person. And the person-to-paint-your-shoelaces should match the dry paint color to the Pantone color on their side.
Alternatively if you know which paint brand will be used you can go to a paint shop and match the dry color.