You can use tris buffer but they have a toxic effect on cells in higher concentrations. If possible you can exchange the buffer like phosphate buffer or you can use tris buffer in very lower concentrations like 10 - 15 uM.
This needs optimization of your protein stability at this concentration of Tris buffer.
You can also try the other buffer suitable for your protein. https://www.hopaxfc.com/en/blog/the-9-best-biological-buffers-for-cell-culture
Choosing a buffer depends upon the objective of your experiment and the nature of your method.
Tris buffer is not always the best choice. Though it is frequently used in biological experiments as it is freely soluble in water, inert in many enzymatic systems (no interactions with other components) and has a high buffer capacity, it may have a series of negative characteristics such as:
a) The pKa value of Tris is 8.06 at 25°C. This means that it is already at the upper end of the pH range of many biological systems (pH 6.0 – 8.0) and that it has a relatively low buffer capacity in the actual physiological pH range (7.0 – 7.5).
b) Tris buffers have a significantly high degree of temperature sensitivity. The effects are therefore very different when Tris is used in the cold room, at room temperature, or at 37°C. This means that the pH value has to be set for the ambient temperature at which it is used.
c) The pH value of a Tris solution is concentration-dependent. On dilution, the pH value decreases by 0.1 pH unit, when diluted from 100 mM to 10 mM.
d) If you are dealing with mammalian cells, then Tris is not the right choice as it is toxic to cells. Tris penetrate cells due to its relatively good fat solubility.
I would suggest you use phosphate buffer instead of Tris buffer for the hydrogen peroxide scavenging assay as it is not toxic to cells, compatible in osmolarity and is insensitive to temperature changes. Phosphate buffer has a high buffering capacity as well.