Praise be to Allah.
What is required is to wash the parts of the body that Allah has enjoined washing in wudoo’ and to wash each part thoroughly so that there is no part of it that the water had not reached.
If there is an injury in the part that one is enjoined to wash, and there is the fear that it will be harmed or healing may be delayed by washing it, then he may wipe over it with water if it is uncovered and he is able to wipe over it. If it is uncovered but he is not able to wipe over it, then he should wash whatever he can of the parts of his body and do tayammum instead for the parts that he cannot wash or wipe over.
If a bandage, plaster or medicine has been put on it that prevents water reaching it, he should wipe over the bandage or plaster.
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.
See also the answer to question no. 142639
With regard to wiping over the socks, if you had previously washed your entire feet or washed whatever you were able to and wiped over the injured part, as described above, then put on the socks when you were in a state of purity, it is permissible for you to wipe over them for a period of one day and one night, if you are not travelling, and for three days and three nights if you are travelling.
Ibn Qudaamah said:
If he put on the khufoof (leather slippers) when in a state of purity in which he did wudoo’ and wiped over the dressing, then it is permissible to wipe over the khufoof. End quote.
Ibn Muflih (may Allah have mercy on him) said:
If he put on khufoof in a state of purity in which he wiped over the plaster, he may wipe over the khufoof.
End quote from al-Furoo‘, 1/198
And Allah knows best.