I have decided to purchase an oak board (1000 SEK at ByggOle until 8/31 or while supplies last...) and cut out the handrails myself. They won't be round but plank-like pieces, similar to the ones already in place, though they are in lacquered pine.
From the board, I will be able to cut 5 pieces that are approximately 12 x 3 x 2500 cm (max). I need three handrails and some other parts around the staircase that need to be replaced with oak. I think it will be great as it will match the kitchen's oak. I plan to oil them with Osmo hard wax oil.
K-rauta has oak handrails from Lundells for about 500 SEK; I'm not sure about the cost of the bends.