A small base die will reduce the case back to SAAMI minimum case dimensions. A small base die will reduce the case diameter and push the shoulder back approximately .003 more than a standard die.
You can adjust the small base die for minimum shoulder bump of .001 to .002 for a bolt action.
I would measure the fired case diameter at three points then full length size the case with your small base die and measure again.
In a semi-auto the resized case should be .003 to .005 "smaller" in diameter than its fired diameter after sizing. This allow the case to spring back from the chamber walls and extract reliably.
In a bolt action the case diameter need not be reduced as much, "BUT" it is the excessive amount of shoulder bump that gives the small base die a bad rap. Meaning case head separations when the die is adjusted per the instructions with the die making hard contact with the shell holder.
Your shoulder bump when sizing is called head clearance when the cartridge is chambered. And excessive head clearance is what causes the case to stretch beyond its elastic limits and separate in the base.
Just remember chambers and resizing dies vary in size and nothing is written in stone. I have a standard Lee .223 die that reduces the case diameter and pushes the shoulder back more than my RCBS small base die.
I use a Hornady cartridge case headspace gauge and measure my "FIRED" cases and set my dies up for minimum shoulder bump.
Below a "FIRED" case in my Hornady gauge and then I set the dies shoulder bump for .003 less than this measurement in my AR15 rifles.
Below is a good diagram of full length resizing and what happens to the resized case. Normally for a bolt action you would want the case shoulder .001 to .002 below the red dotted line. And for a semi-auto .003 to .006 below the red dotted line are the normal should bump standards.
Bottom line, if your small base die is adjusted for minimum shoulder bump and does not reduce the case diameter excessively you "might" be OK using it. BUT this depends on the size of your chamber and resizing die and only case measurements will tell you this.