10th Uhlan Regiment
The proper name is 10 Pułk Strzelców Konnych (10th Mounted Rifles Regiment), but it was indeed commonly referred to as "10 pułk ułanów". After the 1939 campaign, it was reconstituted in the West as an armoured regiment within the 1st Armoured Division under General Stanisław Maczek. In 1944-45, it fought in Normandy (Falaise-Chambois), Belgium, the Netherlands, and Germany. It was considered an elite armoured regiment: black berets, strong cavalry traditions, and a cohesive post-war veterans' community.
Centralne Archiwum Wojskowe (Central Military Archive) has a record of Konrad Wojtysiak, born 1910, rank:
plutonowy (lance corporal) but if you need full personal service file with more detailed information, you have to contact them.
wbh.wp.mil.pl/pl/pages/kontakt-2018-08-28-9y1d/
In the photo you posted your great-granpa is wearing insignia of a
kapral (corporal), so looks like he got promoted during his service in the 1st Armoured.
Also, try this...
polishexilesofww2.org/family-research
... if he was indeed with 1st Armoured (and it makes sense, considering he was with 10th Mounted Rifles before that), there should be detailed records available - it was a famous unit, very well documented. Good luck.

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