2s li-ion packs are widely used without a balance wire or mid-point sensing by reputable companies, but you have to do it exactly like this:
Edit: 0) Make sure the cells are exactly identical, from a high-quality manufacturer, and in identical shape.
1) Charge the cells separately to 4.20V. Verify that they indeed have the same open-circuit voltage (OCV) within 0.01V. 4.19 and 4.18V for example, is ok.
2) Now connect the cells in series, permanently. Don't connect anything to the center tap. Make extra sure there is nothing that can draw current from the midpoint.
3) Now treat it as a fixed product; never charge or discharge the cells separately and never take them apart. You may have the center-tap available for occasional checking with a multimeter, but don't connect anything permanently.
4) Add a little bit leeway to the voltage limits, especially at bottom. For example, for a typical LCO cell, low-voltage cutoff (LVC) is 2.80V and high-voltage cutoff (HVC) is 4.20V. For a two-cell pack, increase the LVC to maybe 3.10V per cell and add a bit of extra margin to HVC side too. So, the final limits might be 2*3.10V=6.20V and 2*4.15V=8.30V. You will lose about 5% of the energy storage doing this but you can expect better lifetime and safety doing so.
For example, Bosch seems to use 4s packs (in their li-ion hand drills) this way without balanced charging or even cell-level LVC, so it clearly works and is clearly safe when done right. When I changed the cells to such a pack after 5 years of use, the cells were still in perfect balance.
If you want to charge/discharge random cells in series (holders for cells you can change, for example), or if you have more than just a few cells in series, you need to monitor the taps between each and every cell to make sure they all stay within the limits while both charging and discharging. Just stopping the charge when one of them reaches 4.20V is fine and easy, but then the others won't get full and will limit the discharge cycle; so actually balancing the cells increases the amount of energy storage.