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Let's consider the process $e^{-} \ (p_1) \ \mu^{-} \ (p_2) \rightarrow e^{-} \ (p_3) \ \mu^{-} \ (p_4)$. In our scriptum, we proved that the matrix element for this process is $$i\mathcal M_{fi} = \underbrace{ie^2 \bar{u}_4\left(p_4\right)\gamma^{\mu}u_2\left( p_2\right)}_{\text{Term 1}} \cdot \frac{1}{q^2} \cdot \underbrace{\bar{u}_3\left( p_3\right)\gamma_{\mu}u_1\left( p_1\right)}_{\text{Term 2}},$$ where $e$ is the (positive) elementary charge.

Now, would it be allowed to swap Term 1 and Term 2? I'm very confident this should be allowed, as both should be scalars, but I wanted to make sure ...

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Yes - they are indeed just numbers.

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