One thing if you do the human robot is that kids that age might not want to participate. They may be shy or not want to be embarrassed about saying the wrong thing. So especially in this kind of demonstration, they may be reluctant to participate in front of everyone. It may work better if you can come up with something they can do in small groups rather than having to interact with you or in front of the whole class. Especially because we all know the best programmers are introverts 
If you choose one of these analogous activities, please make sure that you’re very clear on the purpose of the activity. Kids that age may have trouble connecting the what and the why. Even if they enjoy taking part, make sure you emphasise why you chose the activity and what it represents.
Nerdy swag: mechanical pencils! with the company logo?
I’m thinking that your age group is more like 12-13 years old. 10 is far too young for 6th grade; My daughter is 14 and in the 8th grade.
When I have talked to kids about being in architecture, I start off by asking them what they think I do and take it from there. Most do not really know what it is I do beyond “draw houses”.
I’ve tried activities but have found that the time is typically too limited or that it’s too difficult to orchestrate. You don’t mention how many girls. It sounds like far more than a classroom.
I would suggest a demonstration instead. You might consider making a video showing “a day in the life of”.
Truthfully, I don’t think puzzles will be a hit at all. Anything for a phone is great (such as charms to hang off a case) The robots linked to above are fun, too. Mechanical pencils would be great, as are any quirky items such as thermal-painted things that change colors.
I thought the rule of thumb for estimating ages was grade + 5 years, so that’s where I came up with 10-12 year olds for 6th/7th grade. Probably more like 10-13 if we count late/early starters. Am I wrong?
Class size is around 15.
The “activity” is a specific request. We’re supposed to do something hands-on, and honestly, I’m thinking it’s a hard sell to talk to kids at that age for an hour without some sort of “get out of your chair and do something.” I don’t want to be the boring presenter!
The puzzle idea was the only one I could come up with that I could pull the swag into the actual activity. Phone things / robots / etc are cooler for sure, but not sure how that would help with the hands-on? Maybe I need to give up on that idea.
I think 10 is still a bit young for the grades given, but it is possible. A group of 15 is doable. When you mentioned a university, I was thinking it was going to be various middle schools gathering.
Ok, so start with me. You are a software engineer. What does that mean? What do you do specifically? Do you make apps? (anything having to do with a phone is sure to get their attention).
Is there any swag that involves a little assembly? Two or three steps’ worth of “snap red piece into blue piece” or Tab A into Slot B type of thing? That - plus opening the bag or packaging - should be enough for a simple Human Robot activity.
Then you can talk about the trial and error aspect for the remaining time, which commands didn’t work & why . . . plus a few minutes for Q&A if they seem curious about your specific job.
I was 11 in 6th grade and I was the youngest person in my class.
My rule of thumb when handing out giveaways was to try and make it useful. If it’s useful, then they use it. If they use it, then they remember what you talked about. Something that attaches to a backpack might work, like a zipper-pull, or a mechanical pencil. A stylus (maybe) that attaches to a phone case, or a solar calculator. You’re walking a fine line between something they’ll find useful, or at least non-dorky enough to display, and something they’ll trash.
My dean and I were talking today about some Girl Scouts coming to our college for a STEM-like activity. I’ve used MIT App Inventor to create a simple Android app (it uses a version of Scratch). However, it’s a two- or three-hour project, and as Chronos has said, you’d spend a great deal of time in setup before you can do anything interesting.
If you knew who was coming ahead of time, and could get them to install an app on their phones (and have some spares just in case). I’m sure there are some simple programming apps using turtle graphics or the like. Again, it takes some setup to do that.
I’ve used Dash and Dot robots and some interesting ThinkFun games to introduce programming and logic. How much money do you have? If it’s $20 per person, they have some one-person games (like Rush Hour Traffic Jam you can introduce to them and let them take home.
Or you can get a deck or two of their Visual Brainstorms cards, hand them out and have them pair up to solve them. I’d pick out a few mathematics/logic cards, scan them so you can display to the room, and walk through the solution with the group.