The first big question is where are you doing this? Is it in a metro city/urban setting or in a town in the countryside? The reason for the question is one of cellular coverage / bandwidth availability. For a single video HD stream you’ll be needing in the region of 2Mbps upload which is normally achievable on a single LTE/HDPDA network in my experience (here in the UK). If you can do an on site (or desk based) cellular survey to see which two providers have the best coverage that would help with your planning.
Assuming coverage is good and bandwidth is available, I would suggest a BR1 Slim. This has a single cellular module (with two slim slots in an active/standby configuration so you can use two sims from different operators - one at a time, for better coverage / more capacity) and an inbuilt AP, plus its small and can be powered using a USB Power bank quite easily. I regularily use these from Ravpower http://www.ravpower.com/ravpower-23000mah-portable-charger-external-battery-charger.html and it will run a BR1 all day under normal usage. The whole rig will fit into a laptop bag.
If cellular bandwidth availability is poor, then you move into the requirement for cellular bonding. This becomes a two ended solution in that you need not only a body worn device but also a cloud based endpoint that can receive the SpeedFusion bonded traffic from the multiple remote WAN links on the body worn device and put the original stream back together before forwarding it on to Periscope. My preference for the cloud based endpoint is FusionHub our virtual SpeedFusion appliance, you can run that on a cloud server (like Amazon Web Services or another cloud server provider) and get a short term demo up and running very quickly to test against. Otherwise you will need a physical appliance - something from our Balance range of routers would work great for this role, but it needs to be a Balance 210 or up so that SpeedFusion bandwidth bonding is supported.
When it comes to the multi-cellular body worn device I would probably start with the HD2 Mini. This is a small form factor dual cellular module router (2 x sims per module), that supports SpeedFusion Bonding. It doesn’t come with an inbuilt access point, so I would suggest you add an AP One AC Mini on its LAN for WiFi. Both devices can be powered using a 12V source, and if it was me I would likely use the Ravpower battery pack again as it has a 12V output so you could knock up a cable with a splitter (or buy a cctv power splitter cable) to power both the HD2 mini and the AP One AC Mini from it.
If you need more than dual active cellular connections to achieve the upload bandwidth for the video stream then the next step up with everything fully integrated is the MAX HD4 which has four internal cellular modules and support SpeedFusion Bonding (2 x sims per module) and has an integrated AP, although it might be a little overkill for your application and is a much bigger device physically. Instead I would suggest combining a MAX HD2 Mini and put a BR1 Slim on its WAN port. That combination will give you 3 x active cellular WANs with SpeedFusion support, and the the two routers will happily fit inside a laptop bag. This daisy chain configuration also leaves you with option of using the gear as two completely separate systems at the end of your project (the HD2 Mini and the AP One AC Mini as one set, the BR1 Slim as the other), which is nice.
The other thing to mention is antennas. Our routers come with screw in stick antennas which work fine, but you would probably benefit from extending the cellular antennas out of the bag away from the metal enclosures of the MAX routers and the battery pack. You could either look at 3rd party additional/replacement higher gain antennas or buy a couple of antenna extension leads and mount the stick antennas on the shoulder straps of your bag to reduce interference.
Hope that helps,