Hufschmid played a total of 402 matches for Basel between 1929 and 1950. He scored 83 goals during this time. 268 of these games were in the Nationalliga, 53 in the Swiss Cup and 91 were friendly games. He scored 51 goals in the domestic league, 11 in the Swiss Cup and the other 22 were scored during the test games. He played for six months for Biel-Bienne in 11 games scoring one goal. In the Season 1932–33 Basel advanced to the Swiss Cup Final due to a 5–3 win in the semi-final, in which Hufschmid scored the first goal, against Lausanne Sports. Hufschmid played in the final, which was played in the Hardturm in Zürich against Grasshopper Club. Basel won the final 4–3 and this the club's first ever title win. After suffering relegation to the 1st League in 1938–39, during the 1941–42 season Basel achieved promotion to the Nationalliga as they beat Bern in the play-offs. Hufschmid and Basel qualified for the Swiss Cup final for a second time. This was played on 6 April 1942 in the Wankdorf Stadion against the Nationalliga team Grasshopper Club. The final ended goalless after extra time and a replay was required. The replay was on 25 May, again in the Wankdorf Stadion. Basel led by half time through two goals by Fritz Schmidlin, but two goals from Grubenmann a third from Neukom gave the Grasshoppers a 3–2 victory. After his playing career the Austrian ex-international Anton Schall, who suffered from a rare heart condition, moved to Switzerland and took over Basel as club trainer for the 1946–47 season. Basel advanced to the Cup-Final, which was played in the Stadion Neufeld in Bern on 7 April 1947. Basel won the final 3–0 against Lausanne Sport and thus their second cup title. Schall led Basel to win the Cup, but he died shortly afterwards at the age of 40 years during a workout on the football field. Following this unhappy event captain Hufschmid took over as player/coach and after his playing career he remained as team coach until 1952. He later managed Nordstern Basel and FC Breitenbach.
Swiss Cup winner: 1932–33 as player, 1946–47 as manager
Swiss Cup runner-up: 1941–42 as player
Curiosity
Hufschmid played his last domestic league match on 23 April 1950 in Espenmoos, St. Gallen, as Basel were defeated by St. Gallen. In the Basel's 1950–51 season he played one more match, it was his last active match as football player and this he played as goalkeeper. On 10 August 1950 Football Club Basel played against Eishockey Club Basel. This was a return game for the ice hockey game EHC-FCB in December 1949. The football team won the football match 14–5. Goalkeeper Walter Müller played as striker and he scored six goals.