I got my period at 11 and I didn't tell anyone because I hated having a womans problem. Getting my period was a really big reality check to me. It's when it sunk in that I wasn't going to grow up to be a man. Getting it did make me dysphoric and I was afraid my mom would make a big deal out it and try to celebrate it. I only told her because I needed her to restock, and that was a couple years later. I simply just wrapped it up and threw it out, since she never felt the need to check the trash can she never found out by herself.
I understand getting it brings on the dysphoria, I feel it to. I understand why someone would want to hide it. You don't want the fact that you have lady parts brought to the attention of others. Or even worse for them to talk to you about it. No FTM wants to have to deal with getting periods. Unless you're very lucky, or are at a point in your transition where you don't get them anymore, it's something you have to deal with.
Conformer's methods of dealing with it seem to be adding to the problem. He is obviously unhappy with his methods or he wouldn't be asking for alternatives. Since he is asking for suggestions I assume he can control these impulses enough to change methods. Is creating more steps to the problem really making him feel better? Or is it just making it a bigger problem and breeding more emotional discomfort?
I'm not saying the urge isn't legitimate, but having the impulse doesn't mean you should follow it. If playing in to these unnecessary urges is creating more emotional discomfort I don't see how it's healthy for him to continue.
I am understanding of his problem and related emotions, that's why I offered a logical solution. I think his methods could have the opposite effect. If I lived with an FTM and forgot they could still get periods and came across a wrapper, it would simply jog my memory that they are capable of getting periods. Then I would forget about it a few minutes later. If I came across a bag of used products I would find that really bizarre, and that would be something that would stick with me.