I know this one........
A moderate natural hydraulic lime is what you need. Normally classed as NHL 3.5
Mix this to the ratio of 1 part lime to 2 parts sharp/grit sand and add water. Mixing to a stiff consistency, which feels very rich in lime and will hold together on an inverted trowel. You'll need to chop and pound the mortar to get it mixed and don't put too much water in it, as it will shrink and crack.
Depending on the sand available you might need to add some fine sand if it's too gritty. Normally you would choose a maximum aggregate size half the width of the joint, but if I remember your place is made of coursed rubble, so a 10mm grit sand should do.
I used to buy NHL3 from Mike Wye, but now buy it directly from Breckweg in Germany. It's a very slow, fat lime with a creamy colour. The British don't seem to get on with it and prefer Castle from Hanson, but this is grey and ugly, IMO.
https://www.mikewye.co.uk/product-category/lime-products/?gclid=EAIaIQobChMIw_GktNfP1QIVh7ftCh3zLgtfEAAYASAAEgJ34_D_BwEYou want to put more lime in than less, as a fatty mix is preferable to a lean mix, as it's easier to work with.
So, look at the old mortar and try and determine the aggregate size bearing in mind that the aggregate would have come from within a 10 mile radius of the house and source your quarry, local sand is in keeping with a historic house. Remember they relied on horse drawn carts, so the time taken to freight aggregate would have been kept to a minimum in the 17th Century.
Your old mortar may have charcoal in it and could look like mud.
The charcoal is from the firing of the lime kiln and was mixed in with the fresh burnt lime when it was shoveled out of the kiln. You won't get that with bagged lime and the mud is where the sand was excavated and contained clay. You probably won't be able to get the same consistency as the old mortar, but I would make sure that the colour was similar if the holes are large.
Hydraulic lime has an initial set and a hydraulic set. This means that it will go stiff after a few hours (initial set), but the initial set can be broken if you pound the mortar with a hammer. It will become plastic again and will take the same 30 day period to achieve it's compressive strength, although it will not have the same initial set again and be sof for a while. This means you can leave it covered in the barrow/bucket overnight and come back to it in the morning. This process is called "knocking up" and brickies still use the term when they mix cement mortar, although the process is not the same.
Don't be tempted to use a putty based lime mortar, as this has no frost durability. Putty is for internal plaster and lime wash, NHL is for building outside with.
It's not rocket science, but you'll need to be done and dusted a month before the first frost, as this will blow the mortar apart if it's still wet.
To mix a small quantity you will need a barrow, a shovel, a larry (not the bloke) or a hammer and some elbow grease.