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The phrase "a relatively smaller share" is correct and usable in written English.
It can be used when comparing the size or proportion of a share in relation to something else, indicating that it is smaller in comparison but not necessarily small in absolute terms.
Example: "In the recent market analysis, our company holds a relatively smaller share compared to our main competitors."
Alternatives: "a comparatively smaller portion" or "a lesser share in comparison".
Exact(3)
Most also have a relatively smaller share of dollar debt relative to local-currency debt than they did a decade ago, which will limit the increase in their debt burden when the currency depreciates.
Whilst for those provinces whose wind power capacity is lower, they have a relatively smaller share of the generation source of the province.
However, much of this disease burden is due to non-overweight-related diseases, so a relatively smaller share of the disease burden in the eldest age groups is attributable to overweight.
Similar(57)
Unlike al Qaeda, the FATF said, the Islamic State "currently derives a relatively small share of its funds from deep-pocket donors (relative to its other revenue sources), and thus does not depend principally on transferring money across international borders".
Trade is a relatively small share of total American output.
The United States traditionally devotes a relatively small share of its public wealth to foreign aid.
But, particularly among Hispanics, only a relatively small share get the benefit of that".
— spend only a relatively small share of their high incomes on necessities.
Domestic users everywhere account for a relatively small share (see chart 3).
Multinationals in Colombia still account for a relatively small share of the economy.
First, and most important, a relatively small share of the bill was actually devoted to infrastructure.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com