Just use whatever solder you have. It does not matter. If you are really worried, remove as much of the old solder as you can from the affected joints and apply the new solder.
I'm only a single sample point here but I have a similar opinion. I've always repaired joints with the "wrong solder" (I use lead free, *spits over shoulder and tosses salt*). I suspect it's more important to make sure the final joint looks well shaped and tidy; that _probably_ affects joint performance/lifetime more than using an alloy mix between two different common solder types. I don't think common soldering alloys are unstable-quantity compositions (ie changing composition slightly shouldn't dramatically change performance outside what you can handle, for the most part).
Remember that the alloy in your roll is not the alloy that ends up on your board. Your solder dissolves the pads, pad plating and component leads. Every leg maker plates/coats/dips in a different alloy. HASL PCB makers will probably use whatever solder leftovers they have, up to a certain % of contamination from recovered solder from previous HASLing. There are a lot of acceptable alloys and alloy gradients (I saw a roll of something like 80% lead once?). People who use leaded solder are soldering to unleaded platings on most modern components, some thin some thick, so every component will end up with a different alloy within several %.
There will be edge cases. If you have any doubt: clean away the old solder completely and replace it. Especially if it isn't flowing or does something else weird.
I think I recall some HP scopes coming with a special roll of solder clipped in the back for the repairman to use? I think they did have very specific alloy requirements in certain sections. I don't think this is very common today, everyone wants to make components & PCBs that "work with anything".