Wełniak started playing football in Skra Paterek.[1][2] In 2009, he moved to Czarni Nakło nad Notecią.[1] On 1 March 2013,[3] during testing for Legia's academy,[4] he sustained a fibula and tibia fracture and underwent surgery,[5] with his rehabilitation lasting until November.[3][5] During the 2014–15 season, he signed a contract with Legia Warsaw's academy, where he stayed until the rest of his youth career.[1][6] Before his transfer, Arka Gdynia, Lech Poznań, Lechia Gdańsk and Zawisza Bydgoszcz youth teams were interested in contracting him.[3]
Legia Warsaw II
He made his debut in Legia's second team on 14 June 2017, coming off the substitutes' bench in the 68th minute of a 1–2 home loss to MKS Ełk.[7] On 27 September, he scored two goals during a 3–1 UEFA Youth League victory over Breiðablik's youth team. He scored his first goal for Legia II on 23 May 2018, in the 75th minute of a 2–2 draw with Tur Bielsk Podlaski.[8] In December 2019, he underwent a trial with Stal Stalowa Wola, which did not result in contracting him.[4]
Loan to Siarka Tarnobrzeg
On 15 January 2019,[9] his one-year loan to Siarka Tarnobrzeg was announced by the club.[10][11] Wełniak made his debut in II liga on 16 March 2019 during a 2–2 draw against Znicz Pruszków, during which he came in as a substitute in the 79th minute. On 19 May, he scored the first double of his senior career in a 2–1 home victory over Skra Częstochowa. These two goals were also his first for Siarka.[12]
Return from the loan
On 10 October 2019, in the 57th minute of a 5–0 away loss over Znicz Biała Piska, Wełniak saw a straight red card.[13] In total, during the 2019–20 season, he scored five goals for Legia II, from which two were scored in a match against Ursus Warsaw.[14]
Wigry Suwałki
On 10 January 2020, Wełniak was transferred to I liga side Wigry Suwałki on a two-and-a-half-year deal.[15][16][17] He made his debut on 1 March during a 4–0 away loss over Podbeskidzie Bielsko-Biała.[14] Five matches before the end of that season, he was relegated to II liga with his team.[18] He spent the next season in Wigry.[19] On 27 July 2020, his contract was prolonged for further two years, until June 2024.[20]
In fall 2020, he sustained an injury to the inferior tibiofibular joint and the ligaments of an ankle.[21] Wełniak scored his first two goals on 25 September 2020, during a 2–0 victory with Śląsk Wrocław II, when he came off the bench in the 12th minute of a match as a consequence of an injury sustained by Cezary Sauczek.[19][22][23] Over the course of the two seasons, Wełniak played in 39 matches and scored six goals.[14][19][24]
Podbeskidzie Bielsko-Biała
On 24 July 2021, he moved from Wigry to Podbeskidzie Bielsko-Biała on a three-year deal. There was a clause made in that contract, allowing it to be prolonged.[25][26] He played his first minute in his new team on 17 August, in a goalless draw against GKS Tychy.[27] In total, he played in twenty-four matches in Podbeskidzie and did not score a goal.[27][28]
Loan to Motor Lublin
On 17 January 2023,[29] he was loaned to the I liga side Motor Lublin, with an option to make the move permanent.[30][31][32] where he made his debut in a 3–1 victory over Górnik Polkowice on 5 March. In the 16th minute of that match, he scored the first goal for his new team.[33][34] During his loan spell, Wełniak scored eight goals in 17 matches across all competitions.[28] After the season, Motor advanced to I liga after winning the promotion play-offs.[30][35]
Motor Lublin
His transfer to Motor on a three-year deal was announced on 30 July 2023, following the exercise of the transfer clause in his loan deal.[36][37] On 29 October that year, in the 90th minute of a 2–0 victory over Odra Opole, he scored his first goal in the second division.[38][39] It was also his first goal since the match with Radunia Stężyca, which took place on 13 May.[28][40] On 21 April 2021, in the third minute of a 2–0 away loss over Miedź Legnica, Wełniak scored an own goal.[40][41] After the season, Motor made its advance to Ekstraklasa,[42] where he made his debut in a 1–1 home draw against Korona Kielce on 4 August 2024. On 19 October 2024, in the 86th minute of a 3–4 home loss over Widzew Łódź, he scored his premiere goal in Polish top league.[43]