The hydrogen peroxide was being used as a chlorine neutralizer to lower the FC level.
Though the most obnoxious and sensitive odors are caused by some Combined Chlorine (CC), namely some chloramines (mostly dichloramine and especially nitrogen trichloride and only monochloramine if it gets fairly high), you can most certainly smell outgassed hypochlorous acid chlorine as well, though it is harder to detect and is a very faint bleach-like smell. In a properly managed pool as we prescribe on this forum, you'd only smell the chlorine smell if you went to the pool and churned the water or if you had a cover on it and removed it and smelled right away. If you are in the pool for a while, you might not smell it anymore since your nose will get used to it. It also depends on the person -- some have a more sensitive sense of smell. Also, the 5% FC/CYA ratio of saltwater chlorine generator (SWG) pools is a little harder to smell than the 7.5% FC/CYA ratio of the non-SWG pools. In a spa, it's easier to smell the chlorine because the water is hotter so it outgases faster and the active chlorine level is higher (less chlorine is bound to CYA at hotter temperatures).
When we talk about a properly balanced pool not smelling, we are referring to the obnoxious "pool smell" associated with many commercial/public pools especially indoors. That smell is not pleasant and not what one would call a fresh bleach-like smell.
As for a spa, after a soak when you add chlorine to oxidize your bather waste it is a good idea to leave the cover off for a while (if you can) so that the volatile disinfection by-products can leave the water and not get trapped under the cover. Otherwise when you open the cover the next time you soak you are more likely to smell these "bad smell" products, though even then you can just leave the cover off for a bit before your soak to handle that. Running the jets for part of the time will also help aerate the water to remove such volatiles. As for how long it takes to oxidize the bather waste, the answer is that it depends since some components get oxidized well within an hour (such as ammonia) while other components take many hours (such as urea) with most in between. In general, with hot spa water most of the bather waste is handled within 24 hours in time for the next soak and the majority of it was handled within 12 hours. What isn't handled just builds up to a level where the rate of introduction from you equals the rate of oxidation of it from the chlorine. I'm sure if you were to measure the water after using the spa for weeks that you would measure some level or urea, but it would be a relatively low amount that is very innocuous -- it isn't volatile (and has no smell) and by itself does not cause any harm (it's used in many skin and hair products) and don't forget that it came from you in the first place as the largest nitrogenous component in both sweat and urine.
As for your body smelling of chlorine, you can minimize that by targeting 1-2 ppm FC before your soak. That won't be much different that tap water so more like a shower. In a hot spa, the chlorine will combine with ammonia from sweat very quickly forming monochloramine which is the same chemical used in chloramination so may already be in your tap water -- tap water can be chlorinated with chlorine (hypochlorous acid) or chloraminated with monochloramine. You just need to make sure that you dose after your soak in order to prevent bacteria from growing since your bather load will consume all the chlorine or monochloramine. They won't grow much at all in the hour during your soak (worst-case they quadruple in population but in practice they likely won't grow at all due to the chlorine and/or monochloramine during most of the soak) so it's safe to dose right afterwards to kill them off.
Note that the OP's original issue was noticing a stronger chlorine odor when the FC was 5 compared to when it was 3. So the easiest solution is simply to start off with a lower FC level at the beginning of a soak. The trick is to not go too far and get to zero anytime in between soaks. If the chlorine is too low for too long, then biofilms can form, though as I implied above that doesn't happen in just an hour, but if you go more than 4 hours without chlorine you're at much greater risk, especially 8 hours or more. Once bacteria attach themselves to surfaces and get through their lag phase (sort of like an orientation or adaptation) then they can double in population under ideal conditions every 15-60 minutes. One bacteria can become 65,000 in 4 hours or more than 4 billion in 8 hours. In practice, it's not that extreme, but once a significant amount of bacteria are present they start to form biofilm which are chemicals that protect them and that chlorine does not handle well. If you notice a slimy feel to some spa surfaces, that's possibly biofilm. Even in properly chlorinated spas, it's most commonly found above the water line but there it can be wiped away (a good practice to do whenever you notice it).
