A LW in 38/55 is safer to shoot than a LW in 38/40 or 44/40, assuming the same pressure and barrel weight.
The case head on modern 38/55 is .416 and the case head on 38/40 & 44/40 is .471 and much thinner.
I don't think that the OP will have any problems IF he keeps is bullet selection at 240 gr or less and uses the low end smokeless powder charges developed for the 255 gr bullet and BP, behind the 240> gr bullets.
Why is it I never hear complaints about about how dangerous, using the LW's in 38/40 and 44/40? Loaded to the same pressures with the same SD bullets, the 32/40 and 38/55 are safer, because of the smaller case head and use stronger brass.
The OP's rifle is already built and has probably been shot, to some extent. My LW was 357 Mag when I got it, rebored from a original Win 32 cal barrel. It had been shot for at least, a few years, before I got it, 25 years ago.
It's not in stock but, this would be a good bullet for this LW:
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