For learning, it doesn't matter much how you choose the first action before starting the main loop. That is because the agent doesn't need to learn about transitions to the first state of an episode.
The thing that does matter is that the first action choice should cover all possible actions with probability greater than zero, in order to guarantee convergence. Conceptually, this is not much different to using exploring starts.
However, the usual practice is to have just one active policy for SARSA, typically $\epsilon$-greedy based on Q values learned so far. It is worth noting here, that as Q values change during learning - which happens on each time step - then the policy may also change (when the greedy action choice changes). So even when you use the same rules to derive the policy in SARSA, the actual policy used may vary, even in the middle of the loop. In that respect, the SARSA algorithm uses many policies, but typically only one approach to determining the current policy.
If you are using function approximation and also used a very different rule for the policy for the first action, it is possible you could affect the function approximator through sample bias (your training data has different distribution to target data). This is tricky to put a number on in RL, but is usually ignored in off-policy approximation, so should not put you off if you want to try out ideas of using a different first time step policy.