Connecting two batteries, or I should write cells, in series like this is done all the time.
The negative of one must only contact the positive of the next in series. There are exceptions, mostly dodgy designs, or of course a lead going to a battery monitoring circuit, but mostly it means that the negative poles of both can't be connected directly to the powered device ground.
The other issue is what happens as voltage drops. If the batteries are not very close in capacity, the capacity of the weaker battery will determine end of useful life, and if one discharges to too low a voltage it could be damaging, and if damage could result in a dangerous situation (or just for practical purposes of not ruining the battery) then a battery monitoring system with a low voltage cutoff should be used. In other words unless it is an emergency situation, it's best to always use batteries of the same capacity in series.