Your '98 Mauser could be easily converted to .458 Win. by rebarreling, and opening up the bolt face for the larger cartridge head size. You might also need to open up the action rails to ensure proper feeding. Nothing too complicated for an experienced gunsmith.
To convert to the .375 or the Lott however, would require that the action length be elongated. This has been done countless times over the years, and I've never heard of an action so altered coming apart. But there are right, and wrong ways to go about this. I would be very careful in choosing a smith to do this sort of work.
As to the question about your stock, without seeing it, I couldn't comment on it's suitablity of handling more recoil. Typically, a good glass bedding job will take care of any weaknesses in the stock which might allow it to split. Another consideration is the design/geometry of the stock. Stock design plays a major role in felt recoil to the shooter, as does weight. After lighting off a few of the heavy loads, you may find yourself in the market for a new stock.
Whether you need one or not, large bore rifles are a lot of fun to own, and shoot. I hope you have fun with your new project!
