A few comments.
1] Usually no problem replacing old 18650 cells with new.
2] You really should take your new cells to a professional battery build company and have them do the welding for you. You can purchase cells with tabs already welded on but those may take up too much room in your existing battery case. Under no circumstances should you attempt to solder directly to the end terminals of a Li-Ion battery.
3] There are two types of "protected" cells. Those having only over-current protection and those having low-voltage cutoff boards built in. The cells having only over-current protection are a tiny bit longer than cells without; cells having low-voltage cutoff can be as much as 1.5mm longer than cells without. In general, you are better off purchasing cells that don't have any protection added. The battery management circuit within your battery pack will take care of that for you.
4] It's probably wise to actually test the cells you purchase before you spend the time and money to rebuild your battery pack. Charge them fully, then put a load on each cell and monitor the cell's performance as it discharges. This can be as simple as a resistor on each cell. Bonus points if you are able to actually match the capacity of all the cells going into your rebuilt pack.
You should immediately recharge your cells after discharge-testing them. You don't need to take them all the way to full - around 30% net charge is good.
Testing your cells first is a good way to weed out any duds.
5] Your battery pack may not work after you have replaced the cells. The cure is usually simple: apply a charge voltage to the end terminals on the pack connector. This voltage needs to be current-limited to a low value [50 - 100 mA] with the voltage high enough that to ensure that current flows into the battery. That usually resets the shutdown circuit on the protection board.
Note that when I say "end terminals" on the pack connector, what I mean is the terminals that correspond to the most positive and most negative pins in the connector. These are not necessarily the actual end pins on the connector.