For me, I think if you min-raise in these situations and standard raise in others this is easily exploitable for a thinking player and if I am the BTN or SB I am going to jam ATC on you all day long when you do it. That being said my approach is I don't change anything about my sizing in either of those sitations. For the first if the avg. stack size at my table is >30-40bb I will open to 3x otherwise 2.5x and fold to a SB shove (depending on my holding I may 4bet a 3bet from him, but that depends on my holding). For the second situation I play it the same, I will open to my 3x (or 2.5x depending) and then re-eval the BTN's actions based on my holding and what the blinds do. If the BTN 3bets me and the blinds fold I may play back, if either of the blinds shoves, I may fold not knowing what the player behind will do (and depending on my holding).

I guess my best thoughts on the subject are to not vary your raise sizes because you are afraid of what might happen as someone is going to pick up on it and make you pay for it. Be consistent with your sizing. If you don't like the situation and you feel you holding is marginal, don't be ashamed to fold it. I have folded a lot of marginal holdings to potentially bad sitiuations in some tourneys where in others I have used them to my advantage.