No, it won't cause a balance problem.
Club (cudgel) is a weapon made of wood that does 1-6 damage, 1-3 to larger foes
Bo Stick is a weapon made of wood that does 1-6 damage, 1-3 to larger foes
(AD&D 1e weapons table, from UA p. 27, and PHB p. 37)
Druid weapons proficiencies include: club, dagger, dart, hammer, scimitar, sling, spear, staff
Note: no weapons listing in the PHB, nor in UA, includes "cudgel" so you are going to have to work with your DM about what constitutes a "cudgel" in any case. (We thank @HeyICanChan for the reminder).
Is a bo stick an eligible druid weapon?
Technically, no, based on the weapons proficiency / permitted (p. 19 1e PHB). You'd be better off with an oaken staff, since following the weapons proficiency rules would incur a penalty on your attacks with a bo stick due to non proficiency.
Your weapons proficiency penalty is a -4 to hit for non-proficient weapons. Are you sure you want to do this?
A staff does not accrue that penalty. Further that point, a staff does 1-6 against normal sized and 1-6 against large sized opponents.
Last point: you can probably convince your DM to rule that a staff/club/cudgel are all equivalent if all are made of oak. It's not that far of a reach, and consistent with the use of mistletoe when casting the spell. If the DM will allow that a bo stick is an underpowered staff, and thus usable by druids, so much the better ... if it's made from oak.
If not, I suggest that you use an oaken staff as your "walking stick" to avoid any confusion. Or, go and find the best cudgel you can, and enjoy the benefits of having your shield up (improves AC by 1) when using that cudgel.
There's another way to look at that spell: cudgel as a consumable
Since's it's a first level spell, and cudgel isn't a listed weapon type, another way to view this spell is that the combination of the cudgel and mistletoe and all else creates a temporary magical weapon, which then vanishes once the spell duration is over. For rounds = level, the druid wields a magical weapon, and then it's gone.