Hi Jack, I am not sure that this is a good idea as they are two different types of batteries and may not be compatible. Especially when you go to recharge them. You mention hooking them up in series, plus of one battery to the negative of the other. This will double your voltage to 7.4 volts but will not give you more capacity only more voltage. For more capacity the batteries would have to be hooked in parallel or plus to plus and minus to minus. There are guys on the site that know a lot more about these types of batteries that I do. I would recommend holding off until one of them looks your situation over.
John
John is right.
The tablet cell appears to have protection, while the other is a high discharge version.
You are very likely to have different discharge rates, meaning one will go flat before the other, and with no battery management, you're likely to destroy it.
Charging is another issue.
LiPo batteries are known for catching fire when incorrectly charged, so you will need to do something.
Do yourself a favour and buy something that suits what you need, or are at least the same.
Mark
BTW its not your face (although the toxic fumes may be an issue) it's the house you should be worried about.
One of the few ways to put out a LiPo fire is smother it with sand.