Is الطواف valid if one has a minor impurity (hadath asghar)?

The majority of scholars hold that الوضوء is a condition for the validity of الطواف, based on the hadith: 'الطواف around the House is الصلاة, except that Allah has permitted speaking during it' (narrated by al-Hakim, authenticated by الألباني). However, Sheikh Ibn Taymiyyah and الشيخ ابن عثيمين held the opinion that الوضوء is مستحب but not a strict condition for الطواف validity. If a الحاج loses الوضوء during الطواف, the safer opinion is to renew الوضوء and resume from where the circuit was interrupted.