There is nothing wrong with putting shoes on whilst standing, unless they are the kind of shoes that need some help with the hands to put them on, or it is difficult to put them on whilst standing. In that case it is better to put them on whilst sitting, because that is more appropriate. It was narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) told us that a man should not put on his shoes whilst standing.
Narrated by at-Tirmidhi, 1697; also narrated by Abu Dawood from Jaabir (may Allah be pleased with him), 3606.
Classed as saheeh by al-Albaani in as-Silsilah as-Saheehah, 719
Al-Khattaabi (may Allah have mercy on him) said: It seems that the instruction not to put on shoes whilst standing is because putting them on whilst sitting is easier and more appropriate, and perhaps it might cause you to fall over if you put them on whilst standing. So he instructed that one should sit down and use the hands to help put them. And Allah knows best.
End quote from Ma‘aalim as-Sunan, 4/203
Al-Mannaawi (may Allah have mercy on him) said: The instruction is by way of advice, because putting them on whilst sitting is easier. At-Teebi and others drew the conclusion from this hadeeth that this prohibition applies to footwear that is difficult to put on whilst standing, like the khufoof (leather slippers).
End quote from Fayd al-Qadeer, 6/441
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said concerning the instruction not to put shoes on whilst standing: This applies to shoes that need some effort to put them on the feet, because if a person puts on the shoes whilst standing and they need some extra effort, then he may fall over if he lifts up his foot to fix his shoe. But as for the kind of shoes or sandals that are known nowadays, there is nothing wrong with putting them on whilst standing and that is not included in this prohibition, because the shoes we have now are easy to take off and put on. And Allah is the source of strength.
End quote from Riyadh as-Saaliheen, 1/1953
And Allah knows best.