Safely convert paper wallet to encrypted online wallet
Not completely what you asked for, but if you have a significant amount of money in bitcoin it makes sense to store them on a hardware wallet like trezor, ledger, ... . These cost 100$ or less and are totally worth it for ease of use and peace of mind. 

I would sweep the paper wallets with mycelium and send the btc to your hardware wallet. This completely eliminates the threat of your computer being infected/hacked/etc. Since you have 10 paper wallets, I'm presuming the individual amounts might be ok to store on your phone for a few minutes.

Regarding storage, all addresses on the hardware wallet are generated starting from a 24 word seed. So you could write down 2 or 3 copies of this seed and distribute them in vaults/to trusted people. These 24 words can of course also be encrypted etc. If your hardware wallet breaks, all bitcoins can be retrieved by using these 24 words and a new compatible hardware/software wallet.