Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: If there is a wound on a part of the body that is washed when purifying oneself, there are several scenarios:
(i) It is not covered and will not be harmed by washing. In this case he has to wash it if it is in a place that is to be washed.
(ii) It is not covered but will be harmed by washing but not by wiping. In this case he has to wipe it instead of washing it.
(iii) It is not covered but will be harmed by both washing and wiping. In this case he should do tayammum for it.
(iv) It is covered with a band-aid or the like that is needed. In this case he should wipe over that covering and that will suffice in place of washing that part and he does not have to do tayammum.
Majmoo‘ Fataawa wa Rasaa’il Ibn ‘Uthaymeen, 11/121. See also al-Mughni by Ibn Qudaamah, 1/172-173; al-Mawsoo‘ah al-Fiqhiyyah, 14/273
Based on the above:
If your toe will not be harmed by water, then it must be washed. If it will be harmed by washing but will not be harmed by wiping, then it must be wiped. If it will be harmed by washing and wiping, and has been covered with a dressing, it is sufficient for you to wipe over the dressing.