I have the private keys for multibit HD. Will that work out for me well?
Probably not. MultiBit HD does not allow you to choose which nodes you are connected to so you won't be able to choose which chain you want to use and transact on. It does not provide the (slightly) advanced functionality required to split your coins either.
So electrum is a better choice and gives me all the options I need. correct?
You can go to bitaddress.org, generate a publick - private key pair, print and safe it, send to publick ( btc address) all bitcoins and after all will set down import private key ( that unlock your bitcoins) to any wallet of your choice. This the safest way to be out of comming mess/