You can use Home Strip Paint and varnish Remover for this job as it is totally safe to use in house with no fumes or skin burns. You can check the paint stripping in the projects to get more information.
Once you are back to wood you can sand lightly to make sure it is nice and smooth then apply a water-based wood dye to obtain the colour you want. If usding water-based stain please wear latex gloves as it is a nightmare to get off your skin. Leave to dry then apply a water-based sealer. Polyvine do a great range.
If the mahogany mantle is real mahogany you won’t be able to stain it light oak without bleaching it lighter first. Mahogany is naturally darker than medium oak. Once the paint or varnish has been removed wash down with white spirit and scotch bright to remove any paint striper and paint or varnish still left in the grain. Sheet all the areas up well and apply one of the branded wood bleaches (colourback). I generally use oxalic acid but any branded wood bleach from most decorators’ merchants will do the same. Apply evenly and leave over night remove with plenty of clean water. When dry sand down well as the grain will have risen, you can then apply a spirit stain with a brush and wipe with a sponge to remove excess. Bare in mind when buying stains they are usually made to be put on soft wood not hardwood so if you require a light oak stain then a try a teak stain on mahogany this is more likely to match light oak but it is best to try an inconspicuous area first. If it’s to dark mix mentholated spirits with the stain to make a lighter stain. AS WITH ALL CHEMICALS TAKE PRECAUTIONS WITH YOUR SKIN, EYES, AND VENTALATION.