Well, this is basic statistics. Your uncertainty \$\sigma\$ is probably the standard deviation of instrument if it's unbiased (i.e. if, on average, it estimates correctly), or more generally, the RMS error of the \$i\$th devices from the correct value \$X_0\$:
$$\sigma=\sqrt{\mathbb E\left\{(X_i-X_0)^2\right\}}$$
However, definitely verify this is the definition of "uncertainty" your individual device use! "Uncertainty" is not as strict a term as it should be.
Now, it all depends on how you independent these errors are. Simplest case, the measurement errors are uncorrelated, and all devices are unbiased estimators (so, \$X_0=\mathbb E\{X_i\},\,\forall i\$); then, taking the average of measuments
\begin{align}
\sigma^2_\text{average}&=
\operatorname*{Var}\left(\frac 1N \left(\sum_{i=1}^N X_i\right)\right)\\
&=
\frac1{N^2}\operatorname*{Var}\left(\sum_{i=1}^N X_i\right)
&&\| \tag1\text{factor: quadratic influence on variance}\\
&= \frac1{N^2}\sum_{i=1}^N \operatorname*{Var}\left(X_i\right)
&&\| \tag2\label{indep}\text{independence: variance of sum == sum of var}\\
\sigma_\text{average} &= \sqrt{\sigma^2_\text{average}}\tag3\\
&=\frac1N\sqrt{\sum_{i=1}^N \operatorname*{Var}\left(X_i\right)}\tag4\\
&=\frac1N\sqrt{\sum_{i=1}^N \sigma_i^2}\tag5,\\
\end{align}
in other words, if, and pretty much only if,
- all devices on expectation estimate the true value (that's usually not exactly the case! Usually, measurement devices are designed to have the least variance \$\sigma_i^2\$, not be bias-free, as these are conflicting optimization goals),
- the error is independent for different devices (which is highly unlikely – if one device underestimates the power, it's probably because some aspect of the signal doesn't perfectly fit its design, and then it likely also is underestimated by a different device),
- and you average your measurements,
then you can press down the estimation variance by a factor of the square of how many devices you have. (That's actually, without having much more involved a model, the best you'll be able to do).
If any of the errors are correlated, eq. \$\eqref{indep}\$ doesn't hold, and instead, you get an additional covariance term there – but to estimate covariance between your measurement devices, you'd need multiple relevant measurement standards that you observe with your measurement devices, and that ends up being real workTM.
So, honestly, use your 0.1 dB device. For sanity's sake, this is a bluetooth module! It operates in an indoor environment with unknown moisture, quite probably with moving absorbers ("humans") and reflectors (metal things). 1 dB uncertainty is nothing here; you could probably not make an experiment reproducible enough for that to be a relevant difference in a real-world transmission scenario. So, to answer your original first question:
I'm trying to figure out if there exists a significant difference between measurement instruments
unless you're a certified lab doing measurements where you're legally required to have a lower uncertainty than 0.5 dB, none of this is significant in the application and you can just pick one measurement device do your measurement.
